报告题目：On impulsive reaction-diffusion-advection models in higher dimensions

报告人：王皓 副教授 （University of Alberta）

报告时间：2017年6月13日（星期二）下午14:30

报告地点：复杂系统研究所报告厅

报告摘要：We formulate a general impulsive reaction-diffusion-advection equation model to describe the population dynamics of species with distinct reproductive and dispersal stages. The seasonal reproduction is modeled by a discrete-time map, while the dispersal is modeled by a reaction-diffusion-advection partial differential equation. Study of this model requires a simultaneous analysis of the differential equation and the recurrence relation. When boundary conditions are hostile we provide critical domain results showing how extinction versus persistence of the species arises, depending on the size and geometry of the domain. We show that there exists an extreme volume size such that if the region size falls below this size the species is driven extinct, regardless of the geometry of the domain. To construct such extreme volume sizes and critical domain sizes, we apply Schwarz symmetrization rearrangement arguments, the classical Rayleigh-Faber-Krahn inequality, and the spectrum of uniformly elliptic operators. The critical domain results provide qualitative insight regarding long-term dynamics for the model. Last, we provide applications of our main results to certain biological reaction-diffusion models regarding marine reserve, terrestrial reserve, insect pest outbreak, and population subject to climate change.

*This is a joint work with Mostafa Fazly (University of Texas at San Antonio) and Mark A. Lewis (University of Alberta).

王皓副教授简介：王皓，加拿大University of Alberta副教授。2003年毕业于中国科学技术大学,获数学和计算机科学双理学学士学位，2006年于美国Arizona State University获博士学位; 2007年1月至7月为Arizona State University博士后; 2007年8月至2009年6月为Georgia Institute of Techonology博士后; 2009年7月至2015年6月任Unviersity of Alberta助理教授; 2015年7月至今在University of Alberta任终身副教授。公开发表SCI论文近50篇，主持加拿大自然科学和工程研究基金（NSERC）项目四项。

王皓副教授做精彩报告