2022威廉希尔

非线性分析、微分方程与动力系统系列报告

 

4月28日   9:30-10 :30   腾讯会议号：910 235 156
时间	报告人	Title	邀请人
9:30-10 :30	王明新	Sharp estimates of solutions of free   boundary problems with nonlocal diffusion	薄伟健
4月29日    9:00-11:00   腾讯会议号：401 625 910
时间	报告人	Title	邀请人
9:00-10:00	汪翔升	Global analysis of a viral infection   model with cell-to-cell transmission and immune chemokines	吴事良
10:00-11:00	王金环	Critical mass for a chemotaxis-haptotaxis   model in R^2
4月29日    15:00- 16:00   腾讯会议号：976281645
时间	报告人	Title	邀请人
15:00-16:00	戴斌祥	具时滞影响的Lotka-Volterra竞争-扩散-对流模型	李善兵

 

本期组织：吴事良、李善兵、薄伟健

主办单位：williamhill威廉希尔官网

基金资助：国家自然科学基金、陕西省杰出青年科学基金

联系人： 吴事良 手机:18392190403 E-mail: slwu@xidian.edu.cn

李善兵 手机:18700410622 E-mail: lishanbing@xidian.edu.cn

薄伟健 手机:18394665867E-mail: wjbo@xidian.edu.cn

 

 

报告信息

(以姓氏拼音为序)

 

 

 

 

具时滞影响的Lotka-Volterra竞争-扩散-对流模型

戴斌祥  中南大学

摘要：In this talk, we consider the two-species Lotka-Volterra competition-diffusion-advection model with time delay effect. By utilizing the implicit function theorem, we obtain the existence of at least one spatially nonhomogeneous positive steady state under some conditions on parameters. By analyzing the corresponding characteristic equation, we show the local stability of this spatially nonhomogeneous positive steady state and the occurrence of Hopf bifurcation from it. When there is no time delay, we also study the global stability of the positive steady state. Based on the idea of Chen et al (2018 J. Differ. Equ. 264 5333–5359), the stability and direction of Hopf bifurcation are derived by introducing a weighted inner product associated with the advection rate. Finally, numerical simulations are carried out to verify the theoretical analysis results.

 

报告人简介：戴斌祥，中南大学williamhill威廉希尔官网二级教授、博士生导师；湖南省数学学会常务理事、高等教育与大学数学竞赛工作委员会副主任委员；中国数学会生物数学专业委员会常务理事；入选湖南省新世纪121人才工程人选；主要从事时滞微分方程与离散动力系统、种群生态学与传染病学、反应扩散方程的定性理论与应用等领域的研究，先后在《Nonlinearity》、 《J. Dyn. Diff. Equ.》、 《J. Math. Anal. Appl.》、《Appl. Math. Model》、《Discrete Contin. Dyn. Sys.》、 《Nonlinear Anal.》等国内外权威期刊上发表学术论文160多篇，主持5项国家自然科学基金面上项目、1项国家973计划子课题和多项省部级科研课题，获得湖南省科技进步一等奖和湖南省自然科学一等奖各1项，主编出版教材6部，2020年获得全国宝钢教育基金优秀教师奖。

 

 

 

 

Critical mass for a chemotaxis-haptotaxis model in R^2

王金环 辽宁大学

摘要：In this talk, we consider the Cauchy problem to a chemotaxis-haptotaxis model describing cancer invasion in R2 . The main feature is to prove that 8π is the critical mass on initial data for distinguishing existence and blow-up of solutions to the model. Namely, when the initial mass is less than 8π, we give solutions globally exist by constructing a proper free energy and using the Brezis-Merle type inequality. On the contrary, the fifinite time blow-up of solutions may occur if the initial mass is larger than 8π and the initial second moment is small enough.

 

报告人简介：王金环，辽宁大学williamhill威廉希尔官网教授，博士生导师。研究方向：偏微分方程。2009年获大连理工大学理学博士学位，2010-2012年清华大学博士后，2014-2015年美国 Duke大学访问学者，2020.1-2020.12上海交通大学访问学者；现任中国数学会理事，辽宁省数学会常务理事，辽宁省科技成果评选专家，美国《数学评论》评论员。先后入选辽宁省“兴辽英才计划”青年拔尖人才，辽宁省高校青年学者成长计划、辽宁省百千万人才“千层次”、沈阳市拔尖人才等人才项目。在研国家自然科学基金面上项目1项，已结题国家级项目4项；在研省级课题3项，已结题省级课题3项。在国内外重要学术期刊发表论文近20余篇。获得辽宁省自然科学学术成果奖多项。

 

 

 

 

 

Sharp estimates of solutions of free boundary problems with nonlocal diffusion

王明新  河南理工大学

摘要：In this talk, we study the nonlocal diffusion problems with free boundary.We first give accurate estimates on the longtime behaviors of solution by constructing suitably upperand lower solutions. In particular, for two important kinds of kernel functions, one of which is compactly supported and the other behaves like $|x|^{-\gamma}$ with $\gamma\in(1,2]$ near infinity, some sharp estimates on the longtime behaviors and rates of accelerated spreading are obtained. Then the limiting behaviors of the solution pair of a semi-wave problem and asymptotic dynamics of a nonlocal diffusion problem on half space are given, respectively. Finally, we investigate the limiting profiles of this free boundary problem when the expanding coefficient of free boundary converges to $0$ and $\infty$, respectively.

 

报告人简介：王明新，1990年于北京理工大学获理学博士学位，1990年至1994年在中科院做博士后研究工作，1994年起享受国务院政府特殊津贴，1997年起任博士生导师。现任河南理工大学特聘教授和二级教授。在Proc. London Math. Soc., Trans. Amer. Math. Soc., Indiana Univ. Math. J., Math. Models Methods Appl. Sci., J. Functional Analysis, SIAM系列等国内外核心期刊上发表论文 260 多篇，其中被 SCI检索的有230篇，他引4千余篇次。CRC Press、科学出版社出版和高等教育出版社专著7本，参与编写了科学出版社出版的“数学大辞典”，清华大学出版社出版教材4本。主持完成国家自然科学基金项目9项，在研一项；主持完成省部级项目8项。获得教育部科技进步三等奖2次，江苏省科技进步二等奖和教育部自然科学二等奖各1次，江苏省首届青年科学家奖提名奖，河南省青年科技奖，河南省优秀专家，江苏省优秀研究生指导教师，华英文化教育基金奖。

 

 

 

 

Global analysis of a viral infection model with cell-to-cell transmission and immune chemokines

汪翔升 

University of Louisiana at Lafayette

摘要：We study a viral infection model incorporating both cell-to-cell infection and immune chemokines. Based on experimental results in the literature, we make a basic assumption that the cytotoxic T lymphocytes (CTL) will move toward the location with more infected cells, while the diffusion rate of CTL is a decreasing function of the density of infected cells. We first establish the global existence and ultimate boundedness of the solution via a priori energy estimates. Next, we define the basic reproduction number of viral infection $R_0$ and prove by Lyapunov functional technique and LaSalle invariance principle that the infection-free steady state $E_0$ is globally asymptotically stable if $R_0<1$. When $R_0>1$, then $E_0$ becomes unstable, and another basic reproduction number of CTL response $R_1$ becomes the dynamic threshold in the sense that, if $R_1<1$, then the CTL-inactivated steady state $E_1$ is globally asymptotically stable; and if $R_1>1$, then the CTL-activated steady state $E_2$ is globally asymptotically stable.

报告人简介： 汪翔升毕业于williamhill威廉希尔官网和中国科学技术大学联合高等研究中心。他的研究兴趣包括渐近分析和生物数学等交叉学术领域，最近五年在Adv. Math., J. Differential Equations, J. Math. Biol., J. Math. Pures. Appl., SIAM J. Control Optim.等杂志上发表论文二十余篇。