勷勤数学•专家报告

题      目：Global dynamics of reaction-diffusion systems with a time-varying domain

报  告  人：赵晓强 教授  (邀请人：余虓)

                                              加拿大纽芬兰纪念大学

时      间：5月21日  10：00-11：00

地     点：数科院东楼401

报告人简介:

           赵晓强，加拿大纽芬兰纪念大学数学与统计系教授，该校University Research Professorship荣誉获得者。赵教授先后于1983年和1986年在西北大学数学系获学士和硕士学位，1990年在中国科学院应用数学研究所获博士学位。赵教授长期从事动力系统、微分方程和生物数学相关领域的研究，在单调动力学、一致持久性、行波解和渐近传播速度、主特征值、基本再生数的理论及应用等方面的系列工作受到同行的广泛关注和引用。迄今为止，他已在“Comm. Pure Appl. Math.、 J. Eur. Math. Soc.、 J. reine angew. Math.、 J. Math. Pures Appl.、Trans. Amer. Math. Soc.、SIAM J. Math. Anal.” 等国际知名期刊上发表论文180余篇，并在Springer出版专著“Dynamical Systems  in Population Biology”。赵教授个人主页：https://www.math.mun.ca/~zhao/

摘      要：

       In this talk, I will report our recent research on the global dynamics of a large class of reaction-diffusion systems with a time-varying domain. By appealing to the theories  of asymptotically autononmous and periodic semiflows, we establish the threshold type results on the long-time behavior of solutions for such a system in the cases of  asymptotically bounded and periodic domains, respectively. To investigate the model system in the case of asymptotically unbounded domain, we first prove the global attractivity for nonautonomous reaction-diffusion systems with asymptotically vanishing diffusion coefficients via the method of sub- and super-solutions, and then use the comparison arguments to obtain the threshold dynamics. We also apply these analytical results to a reaction-diffusion model of Dengue fever transmission to study the effect of time-varying domain on the basic reproduction number.

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