International Conference on Reaction-Diffusion Equations and Their Applications to

the Life, Social and Physical Sciences

Program and Abstract(程序册)

May 26-29, 2016Institute for Mathematical Sciences

Renmin University of China, Beijing, China

International Conference on Reaction-Diffusion Equations

and Their Applications to the Life, Social and Physical Sciences

May 26-29, 2016

Website: http://ims.ruc.edu.cn/201605/index.php?cid=80

Conference Venue: Fourth floor, North Canteen (Student Affairs Building,

to the east of Mingde Building), RUC

会议地点：人民大学北区食堂 4 层，即明德楼东侧学生事务楼

Scientific Committee: Henri Berestycki EHESS, PSL Research University, ParisChris Cosner University of MiamiAvner Friedman Ohio State UniversitySuzanne Lenhart University of TennesseeMark Lewis University of AlbertaPhilip Maini Oxford UniversityWei-Ming Ni University of Minnesota, East China Normal UniversityBenoit Perthame Université Pierre et Marie CurieFadil Santosa University of MinnesotaFredric Yui-Ming Wan University of California at IrvineSishen Xie Renmin University , Chinese Academy of SciencesGongqing Zhang Peking University

Organizing Committee: Stephen Cantrell University of MiamiFrancois Hamel Université d`Aix-MarseilleYuan Lou Renmin University & Ohio State UniversityFrithjof Lutscher University of OttawaEiji Yanagida Tokyo Institute of Technology

Local Organizing Committee: Renhao Cui, Xinqi Gong, Litao Han, Yuanyuan Ke, Xiulan LaiYaobin Ou, Qiujin Peng, Hongpeng Sun, Jun Wang

Plenary Speakers:Henri Berestycki EHESSSteve Cantrell University of MiamiChris Cosner University of MiamiYihong Du University of New England at ArmidaleFrancois Hamel Université d`Aix-MarseilleAlexander Kiselev Rice UniversitySuzanne Lenhart University of TennesseFrithjof Lutscher University of OttawaAnna Marciniak-Czochra University of Heidelberg

Kevin Painter Heriot-Watt UniversityKuni Sakamoto Hiroshima UniversityJunping Shi College of William and MaryYoshio Yamada Waseda UniversityEiji Yanagida Tokyo Institute of Technology

Session Speakers (40 minutes): Zerong He Hangzhou Dianzhi UniversityXing Liang University of Science and TechnologyZhigui Lin Yangzhou UniversityBedong Lou Tongji UniversityRui Peng, Jiangsu Normal UniversityYoushan Tao Donghua UniversityChunpeng Wang Jilin UniversityMingxin Wang Harbin Institute of TechnologyShu Wang Beijing University of TechnologyWendi Wang Southwest UniversityYi Wang University of Science and TechnologyZhian WangZhi-Cheng Wang

Hongkong PolytechLanzhou University

Junjie Wei Harbin Institute of TechnologyYaping Wu Capital Normal UniversityXiaoqiang Zhao Memorial University at NewfoundlandFeng Zhou East China Normal UniversityXingfu Zou University of Western Ontario

Session speakers (30 minutes):Shangbing Ai University of Alabama at HuntsvilleXiuqing Chen Beijing University of Posts and TelecommunicationsRenhao Cui Renmin University of ChinaWandi Ding Middle Tennessee State UniversityWeiwei Ding University of Science and TechnologyJian Fang Harbin Institute of TechnologyZhaosheng Feng University of Texas-Rio Grande ValleyRui Huang South China Normal UniversityYuki Kaneko Waseda UniversityYuanyuan Ke Renmin University of ChinaSeonghak Kim Renmin University of ChinaXiulan Lai Renmin University of ChinaHarunori Monobe Tokyo Institute of TechnologyYaobin Ou Renmin University of ChinaYing Su Harbin Institute of TechnologyYixiang Wu University of West OntarioYuxiang Zhang Tianjin University

Registration: May 26 (8:00am-9:00am), Fourth floor, North Canteen (Student Affairs Building, to

the east of Mingde Building), Renmin University of China

Lodging for speakers: Yanshan Hotel, #38 Zhongguanchun Street, Haidian District

北京市海淀区中关村大街 38 号（当代商城旁边） Tel： (010)62563388

Travel reimbursement for plenary speakers: Plenary speakers will be contacted for bank account information.

Contact information:Yuan Lou:Institute for Mathematical Sciences, Renmin University of China, Beijing, ChinaEmail： lou@math.ohio-state.eduPhone: 18800068700

Jun WangInstitute for Mathematical Sciences, Renmin University of China, Beijing, ChinaEmail： wangjunruc@ruc.edu.cn Phone: 13911946007

Schedule: “International Conference on Reaction-DiffusionEquations and Their Applications to the Life, Social and Physical Sciences”

Time: May 26-29, 2016Venue: Fourth floor, North Canteen (Student Affairs Building,

to the east of Mingde Building), Renmin University

May 26, Morning May 26, Afternoon Session I Session II

8:00-9:00 Registration 14:00-14:40

Xiaoqiang Zhao Wendi Wang,

9:00-9:30 Opening ceremony 14:40-15:20

Zhi-Cheng Wang Rui Peng

9:30-10:20 Henri Berestycki 15:20-15:50

Shangbing Ai Yuki Kaneko

10:20-11:10

Alexander Kiselev 15:50-16:20

Break Break

11:10-11:30

break 16:20-17:00

Feng Zhou Junjie Wei

11:30-12:20

Suzanne Lenhart 17:00-17:30

Harunori Monobe Rui Huang

12:20-14:00

Lunch break 17:30-18:00

Seonghak Kim Renhao Cui

May 27, Morning May 27, Afternoon Session I Session II

8:30-9:20 Chris Cosner 14:00-14:40

Mingxin Wang Xingfu Zou

9:20-10:10 Junping Shi 14:40-15:20

Yi Wang Zhian Wang

10:10-10:40

Break 15:20-15:50

Jian Fang Xiulan Lai

10:40-11:30

Eiji Yanagida 15:50-16:20

Break Break

11:30-12:20

Kuni Sakamoto 16:20-17:00

Yaping Wu Youshan Tao

12:20- Lunch break 17:00- Ying Su Yixiang Wu

14:00 17:3017:30-18:00

Weiwei Ding Yuxiang Zhang

May 28, Morning May 28, Afternoon Session I Session II

8:30-9:20 Francois Hamel 14:00-14:40

Shu Wang Zhigui Lin

9:20-10:10 Frithjof Lutscher 14:40-15:20

Chunpeng Wang Bedong Lou

10:10-10:40

Break 15:20-15:50

Xiuqing Chen Yuanyuan Ke

10:40-11:30

AnnaMarciniak-Czochra

15:50-16:20

Break Break

16:20-17:00

Zerong He Xing Liang

11:30-12:20

Kevin Painter 17:00-17:30

Wandi Ding Zhaosheng Feng

12:20-14:00

Lunch break 17:30-18:00

Yaobin Ou open

May 29, Morning 9:00-9:50 Yihong Du9:50-10:40 Yoshio Yamada10:40-11:10

Break

11:10-12:00

Steve Cantrell

May 26, morning

会场：中国人民大学北区食堂 4层 421，在明德楼东侧Room 421, Fourth floor, North Canteen, Renmin University

8:00-9:00 Registration9:00-9:30 Opening ceremony

Chair: Gongqing Zhang9:30-10:20 Henri Berestycki, EHESS, PSL Research University, Paris

The effect of diffusion on a line on Fisher-KPP propagationChair: Steve Cantrell

10:20-11:10 Alexander Kiselev, Rice UniversityDiffusion, mixing and chemotaxis in fluids

11:10-11:30 BreakChair: Wei-Ming Ni

11:30-12:20 Suzanne Lenhart, University of Tennessee

Optimal control of parabolic PDE systems modeling competitive populations

12:20-14:00 Lunch Break

May 26, afternoon

Session I

Room 421, Fourth floor, North Canteen (中国人民大学北区食堂 4层 421)Chair: Shengqiang Liu

14:00-14:40 Xiaoqiang Zhao, Memorial University of NewfoundlandA Nonlocal Spatial Model for Lyme Disease

14:40-15:20 Zhi-Cheng Wang, Lanzhou UniversityMultidimensional traveling fronts in Reaction-Diffusion equations with combustion and non-KPP monostable nonlinearities

15:20-15:50 Shangbing Ai, University of Alabama at HuntvilleTraveling waves for a predator-prey system

15:50-16:20 BreakChair: Fang Li

16:20-17:00 Feng Zhou, East China Normal UniversityClassification of isolated singularities of positive solutions for Choquard equations

17:00-17:30 Harunori Monobe, Tokyo Institute of TechnologyOn traveling wave solutions to curvature flows with external driving force

17:30-18:00 Seonghak Kim, Renmin University of ChinaOn Lipschitz solutions for some forward-backward parabolic equations

18:00 Dinner

May 26, afternoon

Session II

Room 419, Fourth floor, North Canteen (中国人民大学北区食堂 4层 419)

Chair: Ping Liu

14:00-14:40 Wendi Wang, Southwest UniversityMinimal wave speed for a class of non-cooperative diffusion-reaction system

14:40-15:20 Rui Peng, Jiangsu Normal UniversityA Principal Eigenvalue Problem with Large Degenerate Advection

15:20-15:50 Yuki Kaneko, Waseda UniversitySpreading, vanishing and singularity for radially symmetric solutions of a Stefan-type free boundary problem

15:50-16:20 BreakChair: Jingling Wang

16:20-17:00 Junjie Wei, Harbin Institute of TechnologyBifurcation analysis of a diffusive spruce budworm model with delay

17:00-17:30 Rui Huang, South China Normal UniversityAsymptotic stability of non-monotone traveling waves for time-delayed nonlocal dispersion equations

17:30-18:00 Renhao Cui, Renmin University of ChinaA Spatial SIS Model in Advective Heterogeneous Environments

18:00 Dinner

May 27, morning

会场： 中国人民大学北区食堂 4层 421，在明德楼东侧Room 421, Fourth floor, North Canteen, Renmin University of China

Chair: Francois Hamel8:30-9:20 Chris Cosner, University of Miami

Some mathematical models of criminal behavior9:20-10:10 Junping Shi, College of William and Mary

Global extinction of population with Allee effect in advective environment10:10-10:40 Break

Chair: Frithjof Lutscher

10:40-11:30 Eiji Yanagida, Tokyo Institute of TechnologyDynamics of solutions of the Fisher-KPP equation for slowly decaying initial data

11:30-12:20 Kuni Sakamoto, Hiroshima UniversityAn elementary analysis of boundary interactions and bulk diffusion systems

12:20-14:00 Lunch Break

May 27, afternoon

Session I

Room 421, Fourth floor, North Canteen (中国人民大学北区食堂 4层 421)

Chair: Benlong Xu14:00-14:40 Mingxin Wang, Harbin Institute of Technology

Dynamics and patterns of a diffusive Leslie-Gower prey-predator model with strong Allee effect in prey

14:40-15:20 Yi Wang, University of Science and TechnologyDynamics of Almost Periodically Forced Scalar Parabolic Equations on the Circle

15:20-15:50 Jian Fang, Harbin Institute of Technology

Forced waves for the Fisher-KPP equation in moving environment15:50-16:20 Break

Chair: Qianqiao Guo16:20-17:00 Yaping Wu, Capital Normal University

The Stability of Travelling Waves for Autocatalytic ReactionSystems with or without Decay

17:00-17:30 Ying Su, Harbin Institute of TechnologyDelay effect on some diffusive population models

17:30-18:00 Weiwei Ding, University of Science and TechnologySpreading speeds for monostable reaction-diffusion equations with free boundaries in space-time periodic media

18:00 Dinner

May 27, afternoon

Session II

Room 419, Fourth floor, North Canteen (中国人民大学北区食堂 4层 419)Chair: Fengqi Yi

14:00-14:40 Xingfu Zou, University of Western OntarioAsymptotic profiles of steady states for a diffusive SIS epidemic model with mass action infection mechanism

14:40-15:20 Zhian Wang, Hongkong Polytechglobal stability of the predator-prey system with prey-taxis

15:20-15:50 Xiulan Lai, Renmin University of ChinaExosomal microRNAs in lung cancer: a mathematical model

15:50-16:20 BreakChair: Liping Wang

16:20-17:00 Youshan Tao, Donghua UniversityChemotaxis models in complex frameworks

17:00-17:30 Yixiang Wu, University of West OntarioA two strain SIS model with diffusion, spatially heterogeneous coefficients of the reaction part and distinct diffusion rates of the separate epidemiological classes

17:30-18:00 Yuxiang Zhang, Tianjin UniversitySpatial Dynamics of A Reaction-Diffusion Model with Distributed Delay

18:00 Dinner

May 28, Morning

演讲在中国人民大学北区食堂 4层 421，在明德楼东侧Room 421, Fourth floor, North Canteen, Renmin University of China

Chair: Eiji Yanagida

8:30-9:20 Francois Hamel, Université d`Aix-MarseilleMonotonicity in some reaction-diffusion equations

9:20-10:10: Frithjof Lutscher, University of OttawaReaction-diffusion equations for population dynamics in patchy landscapes

10:10-10:40: BreakChair: Junping Shi

10:40-11:30: Anna Marciniak-Czochra, University of HeidelbergStable patterns with jump discontinuity in reaction-diffusion-ODE models with hysteresis and Turing instability

11:30-12:20: Kevin Painter, Heriot-Watt UniversityNavigating the flow: Animal orientation under flows

18:00 Dinner

May 28, afternoon

Section I

Room 421, Fourth floor, North Canteen (中国人民大学北区食堂 4层 421)

Chair: TBA14:00-14:40 Shu Wang, Beijing University of Technology

Some Topics On Nonlinear Fluid-dynamical Equations14:40-15:20 Chunpeng Wang, Jilin University

Semilinear Elliptic and Parabolic Equations with Boundary Degeneracy15:20-15:50 Xiuqing Chen, Beijing University of Posts and Telecommunications

A Note on Aubin-Lions-Dubinskii Lemmas15:50-16:20 Break

Chair: Hua Nie16:20-17:00 Ze-rong He, Hangzhou Dianzi University

Controllability Problem for Population Models with Size-Dependence and Spatial Structure

17:00-17:30 Wandi Ding, Middle Tennessee State UniversityOptimal Control Applied to Native-Invasive Species Competition via a PDE Model

17:30-18:00 Yaobin Ou, Renmin University of ChinaOn Gas-Vacuum Free Interface Problems

18:00 Dinner

May 28, afternoon

Session II

Room 419, Fourth floor, North Canteen (中国人民大学北区食堂 4层 419)

Chair: TBA

14:00-14:40 Zhigui Lin, Yangzhou UniversityThe diffusive West Nile virus model and spatial spreading mechanisms

14:40-15:20 Bedong Lou, Tongji UniversityA diffusive Fisher-KPP equation with free boundaries and time-periodic advections

15:20-15:50 Yuanyuan Ke, Renmin University of ChinaLarge time behavior of solution to a fully parabolic Chemotaxis Chaptotaxis model in higher dimensions

15:50-16:20 BreakChair: Lingfeng Mei

16:20-17:00 Xing Liang, University of Science and TechnologySpreading Phenomena of KPP Equations with Free Boundaries in Almost Periodic Habitat

17:00-17:30 Zhaosheng Feng, University of Texas-Rio Grande ValleyTraveling Wave Phenomena for the Nonlocal Diffusive Single Species System with Allee Effect

17:30-18:00 Open18:00 Dinner

May 29, morning

演讲在中国人民大学北区食堂 4层 421，在明德楼东侧Room 421, Fourth floor, North Canteen, Renmin University of China

Chair: Chris Cosner9:00-9:50 Yihong Du, University of New England at Armidale

Spreading in a shifting environment9:50-10:40 Yoshio Yamada, Waseda University

Asymptotic profiles of solutions for some free boundary problems in ecology

10:40-11:10 Break

Chair: Bei Hu

11:10-12:00 Steve Cantrell, University of MiamiFitness based prey dispersal and prey persistence in intraguildpredation systems

Title and Abstract

Traveling waves for a predator-prey system Shangbing Ai

University of Alabama at HuntvilleE-mail address: ais@uah.edu

Abstract: In this talk, traveling wave solutions for a Holling-Tanner predator-prey system and its generalizations will be discussed. New results on the existence of these solutions will be presented. Their proofs involving upper and lower solutions, Schauder's fixed point theorem, Lyapunov functions, and squeezing technique will be outlined. This is a joint work with Yihong Du and Rui Peng.

"The effect of diffusion on a line on Fisher-KPP propagation"Henri Berestycki

EHESS, PSL Research University – ParisEmail: hb@ehess.fr

Abstract: I will present a system of equations describing the effect of including a line (the "road") with a specific diffusion on biological invasions in the plane. Outside of the road, the propagation is of the classical Fisher-KPP type. We find that past a certain precise threshold for the ratio of diffusivity coefficients, the presence of the road enhances the speed of global propagation. One can determine the asymptotic shape of propagation in every direction influenced by the road. I will discuss several further effects such as transport, reaction on the road or the influence of

various parameters. I will also describe some variants of this system. I report here on results from a series of joint works with Jean-Michel Roquejoffre and Luca Rossi.

Fitness based prey dispersal and prey persistence in intraguild predation systemsStephen Cantrell

University of MiamiE-mail address: rsc@math.miami.edu

Abstract: We establish prey persistence in intraguild persistence systems in bounded habitats under mild conditions when the prey disperses using its fitness as a surrogate for the balance between resource acquisition and predator avoidance. The model is realized as a quasilinear parabolic system where the dimension of the underlying spatial habitat is arbitrary.

A Note on Aubin-Lions-Dubinskii LemmasXiuqing Chen

Beijing University of Posts and TelecommunicationsE-mail address: buptxchen@yahoo.com

Abstract: Strong compactness results for families of functions in seminormed nonnegative cones in the spirit of the Aubin-Lions-Dubinskii lemma are proven, refining some recent results in the literature. The first theorem sharpens slightly a result of Dubinskii (1965) for seminormed cones. The second theorem applies to piecewise constant functions in time and sharpens slightly the results of Dreher and Juengel (2012) and Chen and Liu (2012). An application is given, which is useful in the study of porous-medium or fast-diffusion type equations.

Some mathematical models of criminal behaviorChris Cosner

University of MiamiE-mail address: gcc@math.midmi.edu

Abstract: In recent years there has been considerable interest in developing mathematical models of socioeconomic phenomena in general and criminal activity in particular. One topic that has been treated in some detail is the spatial distribution of criminal behavior, especially burglary. It has been observed that burglaries tend to be clustered in “hotspots” with sizes and locations that do not seem to be determined in an obvious way by the geographic distribution of socio-economic factors. Two influential modeling approaches to understanding the problem of spatial distribution of crime were introduced in the papers (M. B. Short, M. R. D’Orsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi and L. B. Chayes, A statistical model of criminal behavior, Mathematical Models and Methods in Applied Science, 18 (2008), 1249–1267) and (H. Berestycki and J.-P. Nadal, Self-organised critical hot spots of criminal activity, European Journal of Applied Mathematics 21 (2010), 371–399). Models of the first type were initially formulated as agent based models, but continuum limits were derived from those. The resulting continuum models have features somewhat similar to chemotaxis models. Models of the second type of include spatially nonlocal terms and in some cases diffusion. Both types support spatial patterns. Various versions of those models have been studied from the viewpoints of existence theory, bifurcation theory, and traveling waves. This talk will describe some results and problems related to such models.

Stable patterns with jump discontinuity in reaction-diffusion-ODE models withhysteresis and Turing instability

Anna Marciniak-CzochraUniversity of Heidelberg

E-mail address: marciniak@iwr.uni-heidelberg.deAbstract: Coupling diffusion process of signalling molecules with nonlinear dynamics of intracellular processes and cellular growth and transformation leads to reaction diffusion-ODEs models, which differ from the usual reaction-diffusion systems. We show that such systems may lead to a novel pattern formation phenomenon in which diffusion-driven instability causes destabilisation of both constant solutions and Turing patterns. Bistability and hysteresis effects in the null sets of model nonlinearities yield formation of far from the equilibrium patterns with jump discontinuity. We derive conditions for stability of such stationary solutions and consider a global behaviour of the bifurcating branches of nonconstant steady-states. The analysis is illustrated by numerical simulations of an example model from mathematical biology. The talk is based on a joint research with Steffen Harting (Heidelberg University) and Izumi Takagi (Tohoku University).

A Spatial SIS Model in Advective Heterogeneous EnvironmentsRenhao Cui

Institute for Mathematical Sciences, Renmin University of ChinaE-mail address: renhaocui@163.com

Abstract: It's a joint work with Prof. Yuan Lou. In this talk we shall be more interested in the effects of diffusion and advection for a susceptible-infected-susceptible epidemic reaction-diffusion model in heterogeneous environments. The definition of the basic reproduction number R0 is given. If R0 < 1, the unique disease-free equilibrium (DFE) is globally asymptotically stable. Asymptotic behaviors of R0 for advection rate and mobility of the infected individuals (denoted by d I) are established, and the existence of the endemic equilibrium when R0 > 1 is studied. The effects of diffusion and advection rates on the stability of the DFE are further investigated. Among other things, we find that if the habitat is a low-risk domain, there may exist one critical value for the advection rate, under which the DFE changes its stability at least twice as d I varies from zero to infinity, while the DFE is unstable for any d I when the advection rate is larger than the critical value. These results are in strong contrast with the case of no advection, where the DFE changes its stability at most once as d I varies from zero to infinity.

Optimal Control Applied to Native-Invasive Species Competition via a PDE Model,Wandi Ding

Middle Tennessee State University E-mail address: Wandi.Ding@mtsu.edu

Abstract: We consider an optimal control problem of a system of parabolic partial differential equations modelling the competition between an invasive and a native species. The motivating example is cottonwood-salt cedar competition, where the effect of disturbance in the system (such as flooding) is taken to be a control variable. Flooding being detrimental at low and high levels, and advantageous at medium levels led us to consider the quadratic growth function of

the control. The objective is to maximize the native species and minimize the invasive species while minimizing the cost of implementing the control. An existence result for an optimal control is given. Numerical examples are presented to illustrate the results.

Spreading speeds for monostable reaction-diffusion equations with free boundaries in space-time periodic media

Weiwei DingUniversity of Science and Technology

E-mail address: dingww@mail.ustc.edu.cn

Abstract: We study a monostable reaction-diffusion equation of type ut=duxx+ f ( t , x , u) in

space-time periodic media with free boundaries. Such a model may be used to describe the spreading of a new or invasive species with the free boundary representing the expanding front. In cases where f(t; x; u) is periodic in t and radially symmetric in x, and where it is periodic in x and independent of t, such a problem has been studied recently. In both cases, the asymptotic spreading speed is proved to exist by showing that it coincides with the speed of the corresponding semi-wave. In this paper, we focus on space-time periodic media, and develop a new method to determine the spreading speed for free boundary problems without proving a priori existence of semi-wave. This work is in collaboration with Prof. Yihong Du and Prof. Xiang Liang.

Spreading in a shifting environmentYihong Du

School of Science and Technology, University of New EnglandE-mail address: ydu@une.edu.au

Abstract: In this talk I'll discuss some recent results obtained with my collaborators, on the spreading of a new or invasive species in a shifting environment, modelled by a logistic type reaction-diffusion equation with free boundary.

Forced waves for the Fisher-KPP equation in moving environmentJian Fang

Harbin Institute of TechnologyE-mail address: jfang@hit.edu.cn

Abstract: In this talk, we discuss the type, existence and multiplicity of the forced waves for the following Fisher-KPP equation with a moving reaction term

ut=uxx+u (a( x−ct )−u) , x∈Rwhere the smooth function a has limits at infinity.

Traveling Wave Phenomena for the Nonlocal Diffusive Single Species System with Allee EffectZhaosheng Feng

Department of Mathematics, University of Texas--Rio Grande Valley, Edinburg

E-mail address: zhaosheng.feng@utrgv.eduAbstract: In this talk, we are concerned with a nonlocal diffusive single species model with Allee effect. We prove that the model admits positive traveling wave solutions connecting the

equilibrium 0 to some unknown positive steady state if and only if the wave speed c≥2√r ,

where r>0 is the intrinsic rate of increase of the species. For the sufficient large wave speed c, we show that the unknown steady state is the unique positive equilibrium. For two types of convolution kernel functions, we investigate the change of the wave profile as the non-locality increases, and illustrate that the unknown steady state may be a positive periodic solution.The work is a collaboration with B.S. Han and Z.C. Wang.

Monotonicity in some reaction-diffusion equationsFrancois Hamel

Aix Marseille UniversiteE-mail address: francois.hamel@univ-amu.fr

Abstract: The talk is concerned with the Cauchy problem for monostable heterogeneous reaction-diffusion equations with asymptotically homogeneous diffusion and reaction coefficients. I will discuss some of their large-time qualitative monotonicity properties. The question of monotonicity arises in some models of medical imaging. The talk is based on a joint work with E. Grenier (ENS Lyon, France).

Controllability Problem for Population Models with Size-Dependence and Spatial StructureZe-Rong He

Institute of Operational Research and Cybernetics, Hangzhou Dianzi UniversityE-mail address: zrhe@hdu.edu.cn

Abstract: This article investigates the approximate controllability problem of a size- and space-structured population model. The control function acts on an sub-domain and corresponds to the migration of individuals. We first establish the well-posedness of the state system by means of Banach's fixed point reasoning and the theory of parabolic equations, and then confirm the approximate controllability via the unique continuation property of the adjoint system. The desired controller can be determined by a minimizing problem.

Asymptotic stability of non-monotone traveling waves for time-delayed nonlocal dispersion equations

Rui HuangSouth China Normal University

E-mail address: huangrui@m.scnu.edu.cnAbstract: This talk is concerned with the stability of non-monotone traveling waves to a nonlocal dispersion equation with time-delay, a time-delayed integro-differential equation. When the equation is crossing-monostable, the equation and the traveling waves both loss their monotonicity, and the traveling waves are oscillating as the time-delay is big. We prove that all non-critical traveling waves, including those oscillatory waves, are time-exponentially stable, when the initial perturbation around the waves are small. The adopted approach is the technical

weighted-energy method. Numerical simulations in different cases are also carried out, which further confirm our theoretical result. Finally, as a corollary of our stability result, we immediately obtain the uniqueness of the traveling waves for the non-monotone integro-differential equation, which was open so far as we know. This is a joint work with M. Mei, K. Zhang and Q. Zhang.

Spreading, vanishing and singularity for radially symmetric solutions of a Stefan-type free boundary problem

Yuki KanekoWaseda University

E-mail address: y.kaneko5@kurenai.waseda.jpAbstract: We consider a free boundary problem for a reaction-diffusion equation that was proposed by Du-Lin (2010), and discuss spreading, vanishing and singularity for large time behaviors of radially symmetric solutions. If an initial function is defined in an annulus, the inner boundary possibly shrinks until it touches the origin and disappears (called singularity). Hence it is appropriate to introduce a weak solution to study the problem after the disappearance of the inner boundary. Putting a monostable nonlinearity as a reaction term and assuming that the outer boundary is sufficiently far from the inner boundary, we will show that singularity appears in a finite time. Moreover we derive some information on spreading and vanishing.

Large time behavior of solution to a fully parabolic Chemotaxis Chaptotaxis model in higher dimensions

Yuanyuan KeRenmin University of China

E-mail address: keyy@ruc.edu.cnAbstract: This paper deals with the chemotaxis-haptotaxis model of cancer invasion

{u t=Δu− χ ∇⋅(u∇ v )−ξ∇(u∇ v )+u(1−μu−w) , x∈Ω , t>0 ¿ {v t=Δv+v+u , x∈Ω ,t>0 ¿ ¿¿¿¿

¿

in a bounded smooth domain Ω⊂Rnwith zero-flux boundary conditions, where χ , ξ and μ

are positive parameters. It is shown that if μ/ χ is suitably large then for all sufficiently smooth

initial data, the associated initial-boundary-value problem possesses a unique global-in-time

classical solution that is bounded in Ω×(0 ,∞) , and if the initial data w0 is small, w becomes

asymptotically negligible. Moreover, we prove that when domain Ω is convex, ( 1μ, 1μ,0)

is

globally asymptotically stable provided that u0≠0 and thereby extends the result of Hillen et al.

(2013) to the higher space dimensions.

Diffusion, mixing and chemotaxis in fluidsAlexander Kiselev

Rice UniversityE-mail address: alexander.kiselev@rice.edu

Abstract: Many processes in nature and engineering depend on efficient mixing in ambient fluids. The presence of fluid motion can significantly enhance diffusion and mixing, which plays important role in many applications. The examples range from reactions in internal combustion engines to reproduction of marine organisms to nuclear burning in stars.

In this talk, I will discuss a criteria for a class of flows that possess particularly strong diffusion enhancing and mixing processes, called relaxation enhancing flows. Related examples go back to Kolmogorov's construction of weakly mixing flows. The proof of the criterion links mixing with mathematics of quantum mechanics, in particular bounds on the speed of propagation of wave packets.

The relaxation enhancing flows also provide an example of an interesting effect in mathematical biology. The celebrated Keller-Segel equation is a much studied model of chemotaxis: directed motion of cells attracted by a chemical. The Keller-Segel equation has fascinating analytical properties; in particular its solutions can sometimes form delta function singularities in finite time. It turns out that the presence of fluid advection with strong mixing properties can arrest the chemotactic collapse. In particular, the relaxation enhancing flows can lead to such effect.

Exosomal microRNAs in lung cancer: a mathematical modelXiulan Lai

Institute for Mathematical Sciences, Renmin University of ChinaE-mail address: xiulanlai@ruc.edu.cn

Abstract: Lung cancer, primarily non-small-cell lung cancer (NSCLC) is the leading cause of deaths in the United States and worldwide. While early detection significantly improves five-year survival, there are no reliable diagnostic tools for early detection. Several exosomal microRNAs (miRs) are overexpressed in NSCLC, and have been suggested as potential biomarkers for early detection. The present paper develops a mathematical model for early stage of NSCLC with emphasis on the role of the three mostly overexpressed miRs, namely miR-21, miR-205 and miR-155. Simulations of the model provide quantitative relationships between the tumor volume and the total mass of each of the above miRs. Because of the positive correlation between these miRs in the tumor tissue and in the blood, the results of the paper may be viewed as a step toward establishing miRs 21, 205 and 155 as reliable serum biomarkers for NSCLC.

Optimal control of parabolic PDE systems modeling competitive populations.Suzanne Lenhart

University of TennesseeE-mail address: lenhart@math.utk.edu

Abstract: We discuss an important ecological issue of population movement and its distribution in reaction to resources and to competition. We present the choices of directed movement through controlling the advective coefficients in a system of parabolic partial differential equations, modeling two competing species. We seek to maximize population levels while minimizing the cost of controls. In addition to presenting the optimal control analysis, various resource functions and corresponding directed movement choices are shown numerically.

Spreading Phenomena of KPP Equations with Free Boundaries in Almost Periodic HabitatXing Liang

University of Science and TechnologyE-mail address: xliang@ustc.edu.cn

Abstract: In this talk, I want to introduce our work about the spreading phenomena of KPP equations with free boundaries in almost periodic habitat, including traveling waves and spreading speeds.

The diffusive West Nile virus model and spatial spreading mechanisms Zhigui Lin

Yangzhou UniversityE-mail address: zglin68@hotmail.com

Abstract: In this talk, a reaction-diffusion system is proposed to model the spatial spreading of West Nile virus in North America. Infection dynamics are based on a simplified model for cross infection between vector mosquitoes and host birds, and the free boundary is introduced to model and explore the expanding front of the infective region. The spatial-temporal risk index

R0F (t )

, which involves regional characteristic and time, is defined for the simplified model with

the free boundary to compare with other related threshold values, including the usual basic

reproduction number

R0. Sufficient conditions for the virus to vanish or spread are given. Our

results suggest that the spreading or vanishing of the virus depends on the initial number of infected individuals, the area of the infected region, the diffusion rate, and other factors.

A diffusive Fisher-KPP equation with free boundaries and time-periodic advectionsBendong Lou

Tongji UniversityE-mail address: 05213@tongji.edu.cn

Abstract: We consider a reaction-diffusion-advection equation of the form:

ut=uxx−β ( t )ux+ f ( t , u ) for x∈( g( t ) , h( t )) where β ( t ) is a time-periodic

function and f(t,u)$is a Fisher-KPP type of nonlinearity, time-periodic in t, g(t) and h(t) are two free boundaries satisfying Stefan conditions. This equation can be used to describe the population dynamics in time-periodic environment with advection. I will talk about the influence

of the advection parameter β ( t ) on asymptotic behavior of the solutions. It turns out that the

influence is quite different when β ( t ) is a small, or a medium-sized, or a large function.

Reaction-diffusion equations for population dynamics in patchy landscapesFrithjof Lutscher

Department of Mathematics and Statistics University of OttawaE-mail address: flutsche@uottawa.ca

Abstract: Reaction-diffusion equations have been instrumental in theoretical spatial ecology ever since the seminal papers by Fisher, Skellam and others who modelled population dynamics and individual movement and analysed the resulting dynamics. Phenomena such as the speed of spatial spread, the minimal habitat size, and pattern formation conditions are by now well understood, as long as the underlying landscape is homogeneous. Modelling and analysis become considerably more difficult when the landscape is heterogeneous. Should one use Fickian diffusion models or ecological diffusion? How does one analyse the resulting models? And how can one ever hope to parametrize models where landscape quality, movement behaviour, and reproduction vary continuously in space? Landscape ecologists view the environment as consisting of patches between which quality changes but within which quality is homogeneous. This view simplifies continuously varying quality into discrete values, but adds new features to the landscape: interfaces between patches at which the quality of the environment changes abruptly. There is ample empirical evidence that individuals living in such patchy landscapes adjust their movement behaviour to these patch interfaces. How then does one formulate and analyse reaction-diffusion equations for population dynamics in patchy landscapes? In this talk, I will present a recent modelling approach where an individual-level movement model leads to a population-level system of reaction-diffusion equations with discontinuous conditions for thepopulation density at the interfaces between patches. I will outline some analytical tools and re-analyse several famous models in this new framework, for example, the minimal habitat requirements and spreading speeds. I will point to some recent numerical results and outline the research challenges on the way forward to a complete theory.

On traveling wave solutions to curvature flows with external driving forceHarunori Monobe

Tokyo Institute of TechnologyE-mail address: te12001@meiji.ac.jp

Abstract : Mean curvature flow is a geometric flow of hyper surfaces. In 2, 3-dimensional Euclidean spaces, mean curvature flow with external driving force is naturally appeared as a mathematical model describing various biological and physical phenomena, e.g., singular limit of

population dynamic, soap films, grain boundaries, ray optics. Also the interface equation is appeared in some free boundary problems, e.g., mathematical models describing cell locomotion. In this talk, we consider the existence of traveling wave solutions, for curva- ture flow with external driving force, which is a Jordan curve in 2-dimensional space. When there exist traveling wave solutions, we intend to make reference to the shape of traveling wave too. Finally we introduce the application to a free boundary problem describing cell locomotion by using this result.

On Gas-Vacuum Free Interface ProblemsYaobin Ou

Renmin University of ChinaE-mail address: ou@ruc.edu.cn

Abstract: In this talk, I'll present some recent results on the global classical solutions to free boundary problems of hydrodynamic equations when the density of the fluid vanishes at the free boundary. First, we consider the free boundary problem of planar full compressible magnetohydrodynamic equations with large initial data. The global existence and uniqueness of classical solutions is established, and the expanding rate of the free interface is shown. Next, I will show the global existence of classical solutions to the vacuum free boundary problem of isentropic Navier-Stokes equations with gravity force and large initial data. The convergence to the steady state solution is also proved with detailed convergent rates. The major difficulty of these problems is the degeneracy of the system near the free boundary, and the new ingredient is that the smoothness of the solution is always up to boundary.

Navigating the flow: Animal orientation under flowsKevin Painter

Heriot-Watt UniversityE-mail address: K.Painter@hw.ac.uk

Abstract: Sea turtles are famous marine navigators, undergoing long and arduous journeys through the open ocean to nest at isolated island beaches such as Ascension Island in the mid-Atlantic. Any navigational mechanism must not only allow them to locate their goal, but must also allow them to overcome powerful and turbulent currents on route. In this talk I will describe the derivation of a reaction-anisotropic diffusion-advection model based on an underlying individual-based stochastic model that describes animal navigation within a flowing field. I will use the example of navigation to Ascension Island to investigate the critical parameters necessary for navigation, including mean swimming speeds and navigating strength.

A Principal Eigenvalue Problem with Large Degenerate AdvectionRui Peng

Jiangsu Normal UniversityE-mail address: pengrui_seu@163.com

Abstract: In this talk, we shall report our recent work on a principal eigenvalue problem of a linear second order elliptic operator with large degenerate advection. More specifically, we will

study, as the coefficient s→∞ the asymptotic behavior of the principal eigenvalue of the eigenvalue problem−ϕ ''( x )−2 sm' (x )ϕ' ( x )+c( x )ϕ ( x )=λ( s )ϕ( x ),0<x<1

complemented by a general boundary condition. This problem is relevant to nonlinear propagation phenomena in reaction-diffusion equations. The main point is that the advection (or

drift) term m allows natural degeneracy. For instance, m can be constant on[ a ,b ]⊂ [0,1 ]

.Depending on the behavior of m near the neighbourhood of the endpoints a and b, the limiting value could be the principal eigenvalue of

−ϕ ''( x )+c ( x )ϕ ( x )=λϕ ( x ) , a<x<b

coupled with Dirichlet or Newmann boundary condition. A complete understanding of the limiting behavior of the principal eigenvalue and its eigenfunction is obtained, and new fundamental effects of large degenerate advection and boundary conditions on the principal eigenvalue and the principal eigenfunction are revealed. In one space dimension, the results in the existing literature are substantially improved. The talk is based on a joint work with Dr. Maolin Zhou, University of New England, Australia.

An elementary analysis of boundary interactions and bulk diffusion systemsKuni Sakamoto

Hiroshima University E-mail address: kuni@math.sci.hiroshima-u.ac.jpAbstract: We consider systems of N-species bulk diffusion equations complemented with the flux on the boundaries being specified by the interactions among the N-species. The boundary in general has several connected components. Such systems supposedly are models for dynamic activities of proteins in a cell. We carry out elementary analyses on such systems, such as existence of steady states, stability characterizations of steady states, Turing type destabilizations thereof. In these systems, Turing type instability occurs even for cases with equal diffusivity.

On Lipschitz solutions for some forward-backward parabolic equationsSeonghak Kim

Renmin University of ChinaE-mail address: kimseo14@ruc.edu.cn

Abstract: I present the existence and properties of Lipschitz solutions for some forward-backward parabolic equations in all dimensions. Our main approach to existence is motivated by reformulating such equations into partial differential inclusions and relies on a Baire's category method. In this way, the existence of infinitely many Lipschitz solutions to certain initial-boundary value problem of those equations is guaranteed under a pivotal density condition. Under this framework, we study three important cases of forward-backward anisotropic diffusion in which the density condition can be realized and therefore the existence results follow together with micro-oscillatory behavior of solutions. The first case is a generalization of the Perona-Malik model in image processing , the second case that of Hollig's model related to the

Clausius-Duhem inequality in the second law of thermodynamics, and the last one dealing with the diffusion profile even violating Fourier's inequality. This is a joint work with Baisheng Yan.

Global extinction of population with Allee effect in advective environmentJunping Shi

College of William and Mary, USAE-mail address: junpingshi@gmail.com

Abstract: We show that in a spatial population model with strong Allee effect, the population becomes extinct no matter how large the initial population is, if the advection is strong enough or the dispersal rates are in certain range. Hence the extinction equilibrium is globally asymptotically stable, which is quite different from the case of small or no advection that the dynamics is bistable. We will show results in both ODE patch model and reaction-diffusion-advection model.

Delay effect on some diffusive population modelsYing Su

Harbin Institute of TechnologyE-mail address: ysu@hit.edu.cn

Abstract: In this talk, we will show the existence and stability of the spatially inhomogeneous time periodic solutions for some diffusive population models subject to Dirichlet boundary condition. We demonstrate that the spatially inhomogeneous periodic solutions can be bifurcated from the positive steady state for both Logistic and weak Allee type population models. For a special Logistic type model, such bifurcated periodic solutions are shown to be persistent when the parameter is far away from the bifurcation values. This talk is mainly based on some joint works with Junping Shi and Junjie Wei.

Chemotaxis models in complex frameworksYoushan Tao

Department of Applied Mathematics, Donghua UniversityE-mail address: taoys@dhu.edu.cn

Abstract: Motivated by various biological processes, this talk first briefly introduces five typical chemotaxis models: chemotaxis-growth model, chemotaxis-haptotaxis model, chemotaxis-fluid model with signal consumption, chemotaxis-fluid model with chemical production, and chemotaxis model with indirect signal production. Then this talk focuses on addressing a newly proposed Keller-Segel-Navier-Stokes system modeling the phenomenon of broadcast spawning, such as the coral spawning, in which eggs release a chemical that attracts sperm. We study basic mathematical features of such a model for chemotaxis-fluid interaction. More precisely, under some explicit parameter conditions, the boundedness and decay of a classical solution to the corresponding initial-boundary problem is explored in two- and three-dimensional settings.

Semilinear Elliptic and Parabolic Equations with Boundary DegeneracyChunpeng Wang

Jilin UniversityE-mail address: wangcp@jlu.edu.cn

Abstract: In this talk, I introduce our recent researches on semilinear elliptic and parabolic equations degenerating on the boundary, such as optimal regularity, asymptotic behavior and Carleman estimates.

Dynamics and patterns of a diffusive Leslie-Gower prey-predator model with strong Allee effect in prey

Mingxin WangHarbin Institute of Technology

E-mail address: mxwang@hit.edu.cnAbstract: This talk concerns with the dynamical properties and stationary patterns of a diffusive Leslie-Gower prey-predator model with strong Allee effect in the prey population. We first analyze the nonnegative constant equilibrium solutions and their stabilities, and then study the dynamical properties of time-dependent solutions. Moreover, we investigate the stationary patterns induced by diffusions (Turing pattern). Our results show that the impact of the strong Allee effect essentially increases the system spatiotemporal complexity.

Some Topics On Nonlinear Fluid-dynamical EquationsShu Wang

College of Applied Sciences, Beijing University of TechnologyE-mail address: Wangshu@bjut.edu.cn

Abstract: We talk about some topics on nonlinear fluid-dynamical equations. The main topics include: 1)the singularity formation and global regularity of an axisymmetric model for the 3D incompressible Euler and Navier-Stokes equations; 2)Asymptotic limits of compressible Euler-Maxwell equations for electro-magnetic; 3) Quasineutral limit of Drift-diffusion models for semiconductors. The related problems are surveyed and some recent results will also be reviewed.

Minimal wave speed for a class of non-cooperative diffusion-reaction systemWendi Wang

Southwest UniversityE-mail address: wendi@swu.edu.cn

Abstract: In this work, we consider a class of non-cooperative diffusion-reaction systems, which include prey-predator models and disease-transmission models. The concept of weak traveling wave solutions is proposed. The necessary and sufficient conditions for the existence of such solutions are obtained by the Schauders fixed-point theorem and persistence theory. The introduction of persistence theory is very technical and crucial. The LaSalles invariance principle is applied to show that traveling wave solutions connect two equilibria. The nonexistence of traveling wave solutions is proved by introducing a negative one-sided Laplace transform. The results are applied to a prey-predator model and a disease-transmission model with specific

interaction functions. We find that the profile of traveling wave solutions may depend on different eigenvalues according to the corresponding condition, which is a new phenomenon.

Dynamics of Almost Periodically Forced Scalar Parabolic Equations on the CircleYi Wang

University of Science and TechnologyE-mail address: wangyi@ustc.edu.cn

Abstract: In this talk, we focus on the skew-product semiflow generated by a almost periodic spatially-homogeneous scalar reaction-diffusion equation on the circle. The structures of the omega-limit sets, as well as the minimal sets is investigated. We discovered certain new phenomena that reinforce the possible appearance of the almost periodically forced circle flow in infinite-dimensional dynamical systems. This is a joint work with Wenxian Shen and Dun Zhou.

Global stability of the predator-prey system with prey-taxis Zhian Wang

Hong Kong Polytechnic UniversityE-mail address: zhi.an.wang@polyu.edu.hk

Abstract: We consider the global boundedness and stability to the predator-prey system with

prey-taxis. By Moser iteration and LP

-estimates, we show that the intrinsic interaction between

predators and preys in the predator-prey system is sufficient to prevent the population overcrowding without imposing any technical assumption on prey-taxis as done in the existing results. Furthermore, by constructing appropriate Lyapunoval functional, we show that prey-only steady state is globally asymptotically stable if the predation is weak, and the co-existence steady state is globally asymptotically stable under some conditions (like the prey-taxis is weak or prey diffuse fast) if the predation is strong. The exponential decay rates of solutions to the steady states are also derived in our work.

Multidimensional traveling fronts in Reaction-Diffusion equations with combustion and non-KPP monostable nonlinearities

Zhi-Cheng Wang School of Mathematics and Statistics, Lanzhou University

Lanzhou, People’s Republic of ChinaE-mail: wangzhch@lzu.edu.cn

Abstract: In this talk we concern with multidimensional traveling fronts in reaction-diffusion equations with combustion nonlinearity and non-KPP monostable nonlinearity. Our study contains two parts: in the first part we establish the existence and stability of V-shaped traveling fronts in $\Bbb{R}^2$, and in the second part we establish the existence and stability of traveling fronts of pyramidal shape in $\Bbb{R}^3$.

Bifurcation analysis of a diffusive spruce budworm model with delayJunjie Wei

Harbin Institute of TechnologyE-mail address: weijj@hit.edu.cn

Abstract: In this paper, the dynamics of a reaction-diffusion budworm model with delay effect is considered. Existence of constant and nonconstant steady state are shown. The stability of the positive steady state and the existence of Hopf bifurcation are investigated by analyzing the distribution of eigenvalues. The properties of Hopf bifurcation are determined by the normal form theory and center manifold reduction for partial functional differential equations. And global existence of periodic solutions is established by using the global Hopf bifurcation result of Wu. Finally, some numerical simulations are carried out to illustrate the analytical results.

The Stability of Travelling Waves for Autocatalytic Reaction Systems with or without DecayYaping Wu

College of Mathematical Sciences, Capital Normal University E-mail address: yaping_wu@hotmail.comAbstract: Consider the following general autocatalytic reaction system without or with decay

{u t=dΔu−uf ( v )¿ ¿¿¿In this talk we shall talk about our recent progress on the asymptotic stability of traveling fronts for the system without decay (K = 0) and the spectral stability of the wave solution ( Front, Pulse) for the system with strong decay (K > 0 and q > 1). Our arguments are based on Evan's function method, spectral analysis, semigroup estimates and numerical simulation on Evans function mrthod. It's a joint work with Niannian Yan.

A two strain SIS model with diffusion, spatially heterogeneous coefficients of the reaction part and distinct diffusion rates of the separate epidemiological classes

Yixiang WuUniversity of West Ontario

E-mail address: wyx0314y@hotmail.comAbstract: First, it is shown that the model has bounded classical solutions. Next, it is established that the model with spatially homogeneous coefficients leads to competitive exclusion and no coexistence is possible in this case. Furthermore, it is proved that if the invasion number of strainj is larger than one, then the equilibrium of strain i is unstable; if, on the other hand, the invasion number of strain j is smaller than one, then the equilibrium of strain i is neutrally stable. In the case when all diffusion rates are equal, global results on competitive exclusion and coexistence of the strains are established. Finally, evolution of dispersal scenario is considered and it is shown that the equilibrium of the strain with the larger diffusion rate is unstable. Simulations suggest that in this case the equilibrium of the strain with the smaller diffusion rate is stable. This is joint work with Necibe Tuncer and Maia Martcheva.

Asymptotic profiles of solutions for some free boundary problems in ecologyYoshio Yamada

Waseda UniversityE-mail address: yamada@waseda.jp

Abstract: This talk is concerned with free boundary problems which model the invasion or migration of a biological species. The population density of the species is described by a reaction-diffusion equation and a part of the boundary of its habitant is a free boundary, whose dynamics is determined by Stefan condition. Under suitable conditions on nonlinearity in the diffusion equation, the problem admits a unique global solution which exhibits various types of large-time behaviors such as vanishing, spreading or transition. Our main interest lies in asymptotic profiles of solutions for large time and they are depending on the nonlinearity and the boundary condition on the fixed boundary (if it is imposed). We will derive some estimates of the free boundary and density function for large time. Furthermore, we will discuss some interesting asymptotic profiles of density functions.

Dynamics of solutions of the Fisher-KPP equation for slowly decaying initial dataEiji Yanagida

Tokyo Institute of TechnologyE-mail address: yanagida@math.titech.ac.jp

Abstract: This talk is concerned with the behavior of solutions of the Fisher-KPP equation when initial data decay slowly in space. In this case, the large-time behavior of solutions is determined by the decay rate of initial data. In a certain singular limit,the motion of the interface can be described as a level set of a first-order PDE of Hamilton-Jacobi type. By analyzing the Hamilton-Jacobi equation, we can show that there appear various interfacial dynamics. Proofs are based on a comparison method and the analysis of characteristic curves.This is a joint work with Hirokazu Ninomiya of Meiji University.

Spatial Dynamics of A Reaction-Diffusion Model with Distributed DelayYuxiang Zhang

Tianjin UniversityE-mail address: yzhangmath@163.com

Abstract: In this talk, I will report our research on spreading speeds and traveling waves for a class of reaction-diffusion equations with distributed delay. Such an equation describes growth and diffusion in a population where the individuals enter a quiescent phase exponentially and stay quiescent for some arbitrary time that is given by a probability density function. The existence of spreading speed and its coincidence with the minimum wave speed of monostable traveling waves are established via the finite-delay approximation approach. We also obtain the existence of bistable traveling waves in the case where the associated reaction system admits a bistable structure. Moreover, the global stability and uniqueness of the bistable waves are established in the case where the density function has zero tail.

A Nonlocal Spatial Model for Lyme DiseaseXiaoqiang Zhao

Memorial University of NewfoundlandE-mail address: zhao@mun.ca

Abstract: In this talk, I will report our recent research on a nonlocal and time-delayed reaction-diffusion model for Lyme disease with a spatially heterogeneous structure. In the case of a bounded domain, we first prove the existence of the positive steady state and a threshold type result for the disease-free system, and then establish the global dynamics for the model system in terms of the basic reproduction number. In the case of an unbound domain, we obtain the existence of the disease spreading speed and its coincidence with the minimal wave speed. At last, we use numerical simulations to verify our analytic results and investigate the influence of model parameters and spatial heterogeneity on the disease infection risk. This talk is based on a joint work with Xiao Yu.

Classification of isolated singularities of positive solutions for Choquard equationsFeng Zhou

Center for PDEs Department of MathematicsE-mail address: fzhou@math.ecnu.edu.cn

Abstract: We will talk about the classification of isolated singularities of positive solutions to Choquard equation

−Δu+u=I α [up ]uq in RN {0¿ , lim

|x|→∞u( x )=0 ,¿

Where p>0 , q≥1 ,N≥3 , α∈(0 ,N )and

I α [ up ]( x )=∫

RN

u ( y )p

|x− y|N−α dy

We prove the existence of singular solutions in the subcritical case and prove that either the

solution u has removable singularity at the origin or satisfies lim

|x|→ 0u( x )|x|N−2=C

for some constant C. The supercritical case and some case for 0 < q < 1 are also discussed. This is a joint work with Dr. HuYuan Chen.

Asymptotic profiles of steady states for a diffusive SIS epidemic model with mass action infection mechanism

Xingfu Zou Department of Applied Mathematics, University of Western Ontario

E-mail address: xf2zou@gmail.comAbstract: Mass action and standard incidence are two major infection mechanisms in modeling spread of infectious diseases. Spatial heterogeneity plays an important role in spread of infectious diseases, and hence, motivates and advocates diffusive models for disease dynamics. By analyzing a diffusive SIS model with the standard incidence infection mechanism,

some recent works Allen et al (2008) and Peng (2009) have investigated the asymptotic profiles of the endemic steady state for large and small diffusion rates, and the results show that controlling the diffusion rate of the susceptible individuals can help eradicate the infection, while controlling the diffusion rate of the infectious individuals cannot. This work aims to reveal the difference between the two infection mechanisms in a spatially heterogeneous environment. To this end, we consider a diffusive SIS model of the same structure but with the mass action infection adopted, and explore the asymptotic profiles of the endemic steady state for small and large diffusion rates. It turns out that the new model poses some new challenges due to the non-local term in the equilibrium problem and the unboundedness of the nonlinear term. Our results on this new model reveal some fundamental differences between the two transmission mechanisms in such spatial models, which may provide some implications on disease modeling and controls.

This is a joint work with Yixiang Wu.

List of participants

Name Position E_mail AffiliationAlexander Kiselev

Professor kiselev@rice.edu Rice University

Anna Marciniak-Czochra

ProfessorAnna.marciniak@iwr.uni-heidelberg.de

University of Heidelberg

Bang-Sheng Han Student hanbsh13@lzu.edu.cn Lanzhou UniversityBendong Lou Professor lou@shnu.edu.cn Shanghai Normal University

Bin WuAssisstant Professor

bin.wu@bupt.edu.cnBeijing University of Posts and Telecommunications

caoqian Student cqian_526@snnu.edu.cn Shaanxi Normal UniversityChangjing Zhuge Lecturer shuxue1985@foxmail.com Beijing Forestry UniversityChunpeng Wang Professor wangcp@jlu.edu.cn Jilin UniversityChunpeng Wang Professor wangcp@jlu.edu.cn Jilin UniversityDanhua Jiang Student jiangdh15@lzu.edu.cn Lanzhou UniversityEiji Yanagida Professor yanagida@math.titech.ac.jp Tokyo Institute of Technology

Fang LiAssociate Professor

fangli0214@gmail.comCenter for PDE, East China Normal University

Fang Li Post-doc lifangwx@mail.ustc.edu.cnUniversity of Science and Techology of China

Fang-Di Dong Student dongfd15@lzu.edu.cn Lanzhou UniversityFeng Jinping Student rdfjp2012@126.com RUCFeng ZHOU Professor fzhou@math.ecnu.edu.cn East China Normal UniversityFengqi Yi Professor fengqi.yi@aliyun.com Harbin Engineering UniversityFrancois Hamel Professor francois.hamel@univ-amu.fr Aix-Marseille UniversityFrithjof Lutscher Professor flutsche@uottawa.ca University of Ottawa

Fuxiang Li Student Fuxiang_li@163.comUniversity of Science and Technology Beijing

Christopher Cosner

Professor gcc@math.miami.edu University of Miami

Guanghui Zhang Lecturer guanghuizhang@hust.edu.cnHuazhong University of Science & Technology

Guo Yuxiao Lecturer guoyuxiaolove@163.comHarbin Institute of Technology at Weihai

Guodong Wang Student 1106452445@qq.com AMSS，CAS

Haifeng Hu Post-doc huhf836@nenu.edu.cnCenter for Partial Differential Equations, ECNU

Harunori Monobe

Post-doc te12001@meiji.ac.jpSchool of Science, Tokyo Institue of Technology

Henri Berestycki Professor hb@ehess.fr EHESSHongmei Cheng Student hmcheng@mail.bnu.edu.cn Beijing Normal University

Hua NieAssociate Professor

niehua@snnu.edu.cn Shaanxi Normal University

Huang Xia Student xhuang1209@gmail.com East China Normal University

Huicong Li Post-doc hli7@tulane.eduCenter for PDE, East China Normal University

Jiabing Wang Student wangjb2014@lzu.edu.cn Lanzhou UniversityJia-Feng Cao Student caojf07@lzu.edu.cn Lanzhou UniversityJiajia Shi Student 1358784213@qq.com East China Normal UniversityJian Fang Professor jfang@hit.edu.cn Harbin Institute of TechnologyJian Liu Student jian_liu1990@163.com Ordnance Engineering College

Jian YangAssisstant Professor

yangjian86419@126.com University of Jinan

Jianwen Jia Professor jiajw.2008@163.com Shanxi Normal University

Jian-Wen SunAssociate Professor

jianwensun@lzu.edu.cn Lanzhou University

Jing Ge Student gejing2150@163.com Yang Zhou University

Jingjing XiangAssociate Professor

xiangjingjing66@126.comXi`an univercity of Architecture & Technology

Jinliang WangAssociate Professor

jinliangwang@aliyun.com Heilongjiang University

Junfeng He Student hejunfeng8804@163.com Capital Normal UniversityJunjie Wei Professor weijj@hit.edu.cn Harbin Institute of TechnologyJunping Shi Professor jxshix@wm.edu College of William and Mary

Junyuan YangAssociate Professor

yangjunyuan00@126.com Shanxi University

Kejun ZhuangAssociate Professor

zhkj123@163.comAnhui University of Finance and Economics

Kevin PainterAssociate Professor

K.Painter@hw.ac.uk Heriot-Watt University

Keying Song Student 17801052630@163.comUniversity of Science and Technology Beijing

Lei WeiAssociate Professor

wlxznu@163.com Jiangsu Normal University

Li dandan Student 2140502114@cnu.edu.cn Capital Normal UniversityLi Rui Student liruicxis@163.com Renmin University of ChinaLi Shanbing Student lishanbing2006@163.com Shaanxi Normal University

Li Xiang Student sizuin@live.cnNational Universary of Science and Technology

Li Xiaomeng Student 85879262@qq.com RUCLi xiaoshuang Student 873927345@qq.com Shaanxi Normal UniversityLiangchen Li Student llc0610@126.com Ordnance Engineering CollegeLili Liu Lecturer liulili03@sxu.edu.cn Shanxi UniversityLin Zhao Student zhaoandzhang@126.com Lanzhou University

Linfeng MeiAssociate Professor

lfmei@outlook.com Henan Normal University

Liping WangAssociate Professor

lpwang@math.ecnu.edu.cn East China Normal University

Meihua WeiAssociate Professor

wei_meihua@163.com Yulin University

Min Zhu Student min_zhuly@163.com Yangzhou UniversityMingtao Li Student limingtao18@126.com Shanxi UniversityMingxin Wang Professor mxwang@hit.edu.cn Harbin Institute of TechnologyNingkui Sun Student sunnk1987@163.com Tongji University

Niu BenAssociate Professor

niubenhit@163.comHarbin Institute of Technology at Weihai

Pengfei Lu Student jacinto@snnu.edu.cn Shaanxi Normal UniversityPing Liu Professor liuping506@gmail.com Harbin Normal University, HarbinQi An Student 18745746090@126.com Harbin Institute of Technology

Qianqiao GuoAssociate Professor

gqianqiao@nwpu.edu.cnNorthwestern Polytechnical University

Qihong Shi Lecturer shiqh03@163.com Lanzhou university of technology

Renhao CuiAssociate Professor

renhaocui@163.com Renmin University of China

Robert Stephen Cantrell

Professor rsc@math.miami.eduUniversity of Miami and Renmin University of China

Rui Huang Professor huangrui@m.scnu.edu.cn South China Normal UniversityRui Peng Professor pengrui_seu@163.com Jiangsu Normal UniversitySadia Arshad Post-doc sadia_735@yahoo.com Chinese Academy of SciencesSakamoto, Professor kuni@math.sci.hiroshima- Hiroshima University

Kunimochi u.ac.jpSeonghak Kim Post-doc kimseo14@ruc.edu.cn Renmin University of China

ShangbingAssociate Professor

ais@uah.eduUniversity of Alabama in Huntsville

Shengqiang Liu Professor sqliu@hit.edu.cn Harbin Institute of TechnologyShiliang Wu Professor slwu@xidian.edu.cn Xidian universityshiyao Student qq315155637@snnu.edu.cn Shaanxi Normal UniversityShu WANG Professor wangshu@bjut.edu.cn Beijing University of TechnologySun Xiuli Student sxl891123@163.com Beijing Normal University

Suzanne Lenhart Professor lenhart@math.utk.eduUniversity of Tennessee and NIMBioS

Tao Zhou Student tzhou910@hotmail.comUniversity of Science and Techology of China

Tatsuki Mori Post-doc tatsuki7837@agmail.com East China Normal UniversityTianHuijie Student 823584670@qq.com SHAANXI NORMAL UNIVERSITY

Wanbiao Ma Professor wanbiao_ma@ustb.edu.cnUniversity of Science and Technology Beijing

Wandi DingAssociate Professor

wandi.ding@mtsu.eduMiddle Tennessee State University

Wang Xin lei Student 525828529@qq.com Shaanxi Normal University

Wang,linaAssisstant Professor

wanglina147@126.comBeijing Technology and Business University

Wan-Tong Li Professor wtli@lzu.edu.cn Lanzhou University

Wei Wang Student wei___wang@163.comUniversity of Science and Technology Beijing

Weihua Jiang Professor jiangwh@hit.edu.cn Harbin Institute of Technology

Wei-Ming Ni Professor weiming.ni@gmail.comEast China Normal University & University of Minnesota

WEIWEI DING Post-doc dingww@mail.ustc.edu.cn University of New England

Wen-Bing Xu Student xuwb08@lzu.edu.cnSchool of Mathematics and Statistics

Wendi Wang Professor wendi@swu.edu.cn Southwest University, China

Xian ZhangAssociate Professor

zhangx663@126.com Heilongjiang University

xiao-bing zhangAssociate Professor

zhangxb@lut.cn Lanzhou university of technology

Xiaoqing He Post-doc sakula1213@gmail.comCenter for Partial Differential Equations

Xiaoyan ZhangAssociate Professor

zxysd@sdu.edu.cn Shandong University

Xin Wu Student wuxin8710180@163.com Beijing Normal University

Xinqi GongAssociate Professor

xinqigong@ruc.edu.cn Renmin University of China

Xinyue Zhao Student zhaoxinyue9293@163.com Renmin University of ChinaXiongxiong Bao Student baoxx09@lzu.edu.cn Lanzhou UniversityXiulan Lai Post-doc xiulanlai@ruc.edu.cn Renmin Uinversity of China

Xiuqing Chen Professor buptxchen@yahoo.comBeijing University of Posts and Telecommunications

Xu Huicai Student 514485636@qq.com RUC

Xu YoujunAssociate Professor

youjunxu@163.com 南华大学Xueli Bai Lecturer xlbai2015@nwpu.edu.cn

Northwestern Polytechnical University

Xun Cao Student 891953756@qq.com Harbin Institute of Technology

YAN Niannian Student ynn0929@163.comDepartment ofmathematics Capital Normal University

Yang Bowen Student ybw2015goodluck@163.com Harbin Normal UniversityYang Wang Student ywang@mail.bnu.edu.cn Beijing Normal UniversityYang Wang Professor yangwang79@126.com Hangzhou Dianzi University

Yantao Wang Student wangyt@mail.sustc.edu.cnSouthern University of Science and Technology

Yaobin OuAssociate Professor

ou@ruc.edu.cn Renmin University of China

Yaping Wu Professor yaping_wu@hotmail.com Capital Normal UniversityYaying Dong Student sxsbjsying@163.com Northwest University

Yi Li Professor yi.li@csun.eduCalifornia State University, Northridge

Yi Wang Professor wangyi@ustc.edu.cnUniveristy of Science and Technology of China

Yihong Du Professor ydu@une.edu.auUniversity of New England, Australia

Ying SuAssociate Professor

ysu@hit.edu.cn Harbin Institute of Technology

Yingjie ZhuAssisstant Professor

yingjiezhu2012@163.com Changchun University

Yingli Pan Student 957829365@qq.com Harbin Institute of TechnologyYiting Wu Student yitingly@126.com RUCYixiang Wu Post-doc wyx0314y@hotmail.com University of Western OntarioYoshio Yamada Professor yamada@waseda.jp Waseda UniversityYoushan Tao Professor taoys@dhu.edu.cn Donghua UniversityYuan He Lecturer hey@lzu.edu.cn Lanzhou UniversityYuan Lou Professor lou.8@osu.edu Renmin University & Ohio StateYuanwei Qi Professor yuanwei.qi@ucf.edu University of Central Florida

Yuanyuan KeAssociate Professor

keyy@ruc.edu.cn Renmin University of China

Yuanyuan Li Student yuanyuanlimath@163.com Harbin Normal UniversityYue Wang Student wy2006518@163.com Renmin University of China

Yuki KanekoAssisstant Professor

y.kaneko5@kurenai.waseda.jp

Waseda University

Yulan Wang Professor yulanwang1202@gmail.comSchool of Science, Xihua University

Yunfeng Geng Student 171144519@qq.com RUC

Yuxiang ZhangAssisstant Professor

yzhangmath@163.com Tianjin University

Ze-Rong He Professor zrhe@hdu.edu.cn Hangzhou Dianzi UniversityZhang Liang Student zhangll-2009@lzu.edu.cn Lanzhou Universityzhanghao Student nerazzurri-zh@163.com capital normal universityZhao Yonggang Lecturer ygzhao@aliyun.com Henan Normal University

Zhao, Xiaoqiang Professor zhao@mun.caMemorial University of Newfoundland

Zhaohai Ma Student zhaohaima@mail.bnu.edu.cn Beijing Normal University

Zhaosheng Feng Professor zhaosheng.feng@utrgv.eduUniversity of Texas-Rio Grande Valley

zhenguo luoAssociate Professor

robert186@163.com Hengyang Normal University

Zhen-Hui Bu Student buzhh14@lzu.edu.cn Lanzhou University

Zhian WangAssisstant Professor

mawza@polyu.edu.hk Hong Kong Polytechnic University

Zhigui Lin Professor zglin68@hotmail.com Yangzhou UniversityZhiguo Wang Lecturer zgwang@snnu.edu.cn Shaanxi Normal University

陈方媛 Student chenfangyuan666@126.com 北京建筑大学杜祯敏 Student 1602089076@qq.com 中国人民信息学院方亦豪 Student 2011202401@ruc.edu.cn

Information School, Renmin University of China

高淑敏 Student 743772702@qq.com Shaanxi Normal University

郭改慧 Associate Professor

guogaihui@sust.edu.cn 陕西科技大学胡钡 Professor b1hu@nd.edu 人民大学，圣母大学姜红岩 Student 961089322@qq.com Shanghai Normal University

李辰潼 Student lichentong1989@163.com 数学与统计学院 西安交通大学李青 Student liqing.cnu@gmail.com 首都师范大学

李岩 Student liyan1989@stu.xjtu.edu.cn 西安交通大学梁建秀 Associate

Professorljx6969@163.com 山西省晋中学院 数学学院

林勇 Professor linyong01@ruc.edu.cn 人民大学刘娟 Student juanliu@ruc.edu.cn 信息学院刘钱 Student 1498991649@qq.com Renmin of University

刘迎东 Associate Professor

ydliu@bjtu.edu.cn 北京交通大学邱胜男 Student 645268118@qq.com 中国人民大学信息学院宋倩 Student 1595303943@qq.com SHAANXI NORMAL UNIVERSITY

苏远航 Student suyh14@lzu.edu.cn 兰州大学苏远航 Student suyh14@lzu.edu.cn 兰州大学王高雅 Student 81665812@qq.com Shanghai Normal University

王华颖 Associate Professor

hywang@heuet.edu.cn 河北经贸大学王雅璇 Student sx11yxw@163.com Capital Normal University

徐本龙 Professor bxu@shnu.edu.cn Shanghai Normal University

闫丽丽 Student 2015103426@ruc.edu.cn 人民大学闫念念 Student ynn0929@163.com 首都师范大学袁海龙 Student 422055696@163.com SHAANXI NORMAL UNIVERSITY

原新鹏 Student yuanxinpeng1987@163.com 北京理工大学张聪晖 Student 422055696@qq.com SHAANXI NORMAL UNIVERSITY

张丽霞 Student 1428263206@qq.com SHAANXI NORMAL UNIVERSITY

Local information about lodging, lecture hall and local transportation:

1. Lodging for speakers: Yanshan Hotel, #38 Zhongguanchun Street, Haidian District 北京市海淀区中关村大街甲 38 号（当代商城旁边）, 燕山大酒店

2. Location of lecture hall: Fourth floor, North Canteen (Student Affairs Building, to the east

of Mingde Building), Renmin University of China

(人民大学北区食堂 4 层，即明德楼东侧学生事务楼)

3. Local transportation

(1) The Capital International Airport首都国际机场Subway: Take the airport express (fast track), get off at Sanyuan Bridge station, then transfer to subway line 10, and get off at Suzhou Street station, then exit from C gate (the South east exit), and walk to Renmin University.

地铁：乘坐机场快轨（三元桥方向）在三元桥站下车，换乘地铁十号线，在苏州街站下车（C 东南口出），步行至中国人民大学西门。

Public bus: Take the airport bus to the direction of Gongzhufeng, and get off at Youyi Hotel stop, and then walk to the east gate of Renmin University. By urban Taxis: this costs approximately 100 RMB.

地面公交: 乘坐机场大巴公主坟线，在友谊宾馆站下车，步行至中国人民大学东门。 出租：打车约 100 元人民币。

(2) Beijing Railway Station北京站Subway: Take subway line 2 (internal) and get off at Xizhimen station, and then transfer to subway line 4 to the direction of Anhe Bridge, get off at Renmin University station, exit from A1 gate and walk to Renmin University. By taxis, it costs about 60 RMB.

地铁：乘坐地铁 2 号线（内环），在西直门站下车，换乘地铁 4 号线（安河桥北）方向，在人民大学站下车（A1 口出），步行至中国人民大学东门。

出租车：打车费用约 60 元人民币。

(3) Beijing West Railway Station北京西站Subway: Take subway line 9 and get off at the National library station, and then transfer to subway line 4 in the direction of Anhe Bidge North, get off at Renmin University station from the A1 gate, and walk to the east gate of Renmin University.

地铁：出站后乘坐地铁 9 号线（国家图书馆方向），在国家图书馆站下车，换乘地铁 4 号线（安河桥北方向），在人民大学站下车，（A1 口出）。步行至中国人民大学东门。

Public bus: ① Take the No. 374 bus, get off at Wanquanzhuang stop, and walk to the west gate of Renmin University. ② Take the special No. 18 or 6 bus, get off at Renmin University stop, and then walk to the east gate of Renmin University. By taxis; this costs approximately 35 RMB.

公交：①在北京西站公交站乘坐 374 路公交，在万泉庄站下车，步行至中国人米大学西门。 ②在北京西站公交站乘坐特 18 路或特 6 路，在人民大学站下车，步行至中国人民大学东门。 出租：打车费用约为 35 元人民币。

(4) Beijing South Railway Station北京南站Subway: Take subway line 4 in the direction of Anhe Bidge North, get off at Renmin University station from the A1 gate, and walk to the east gate of Renmin University.

地铁：乘坐地铁 4 号线（安河桥北方向），在人民大学站下车，（A1 口出），步行至中国人民大学东门。

Public bus: Take the special No. 5 bus, get off at Wanquanzhuang stop, and then walk to the west gate of Renmin University. By taxis; this costs about 60 RMB.

公交：在北京南站南广场乘坐特 5 路公交，在万泉庄站下车，步行至中国人民大学西门。 出租：打车费用约为 60 元人民币。