“数理论坛”第123期：Dynamics of two reaction-diffusion population models

报告题目

Dynamics of two reaction-diffusion population models

报告时间

2019年11月6日下午16：00

报告地点

东区综合楼A1404会议室

报告人

陈玉明（加拿大罗瑞尔大学教授）

报告人

简介

陈玉明，分别于1991年和1994年从北京大学获应用数学学士学位和硕士学位，并于2000年从加拿大约克大学（York University）获理学博士学位，2000年9月至2001年6月在加拿大阿尔伯塔大学（University of Alberta）做博士后。从20001年7月起，一直任教于加拿大罗瑞尔大学(Wilfrid Laurier University)。现为该校数学系正教授、博士生导师。主要研究兴趣为动力系统和泛函微分方程理论及其在生物数学和神经网络中的应用。已在包括SIAM Journal on Mathematical Analysis, Transactions on the American Mathematical Society, Nonlinearity, Journal of Differential Equations, Physica D, Proceedings of the American Mathematical Society, Mathematical Biosciences, Neural Networks等国际著名刊物发表论文百余篇，其成果被同行广泛引用，曾获安大略省科技与创新部早期研究者奖。主持了4项加拿大国家自然科学与工程理事会(NSERC)科研基金项目，参与了3项中国国家自然科学基金面上项目。积极参与高质量人才如硕士生、博士生、博士后的培养。陈教授与中国学者有广泛交流与合作。

报告摘要

In this talk, we consider two reaction-diffusion population models. The first is about the growth of a species in shifting habitats due to unbalanced resources. We study some nonlinear propagation phenomena. Depending on the size of the shifting speed relative to the minimum traveling wave speeds of the limiting systems at both negative and positive infinities, there are three scenarios: 1) The limiting systems at both negative and positive infinities control the propagation characteristics; 2) the travelling wave speed of the limiting resource-rich system affects the asymptotic propagation properties of solutions; 3) very large speed of resource movement will weaken the control of the limiting resource-rich system on the persistence or upward convergence of the asymptotic propagation of solutions. The second model describes a single species with different mature-immature habitats accounting for a scenario where the boundaries are hostile to the species. We obtain threshold results under the supremum norm, which are greatly different from the existing ones on other evolution equations in unbounded domains or the whole space. The results are obtained by employing new domain decomposition methods and dynamical system approaches. They are also applied to two examples with the Ricker birth function and with the Mackey-Glass birth function.

邀请人

郭上江 教授

2019年10月28日