报告题目：Existence, multiplicity, shape and attractivity of heterogeneous steady states for bistable reaction-diffusion equations in the plane

报 告 人：易泰山教授（中山大学）

报告时间：2019年5月10日 14:40

报告地点：数统院307学术报告厅

报告摘要：

We consider a class of bistable reaction-diffusion equations in the plane. First we introduce a partition of the plane into infinitely many sectors and consider Dirichlet problems in these sectors. By  establish some \textit {a priori} estimates for nontrivial solutions to these sub-systems, we obtain the existence and attractivity of  a heterogeneous steady state of the Dirichlet problem in each of the sectors and  prove the existence of a maximum positive steady state and describe the asymptotic behaviours of positive steady states at the infinities. We also estimate $\omega-$limit sets at the vicinities of the boundaries of the sectors near origin and at infinities. Further assuming the sub-linearity for the reaction term, we obtain the uniqueness and attractivity of a heterogeneous steady state by applying the dynamical and sliding methods. These results help us describe the multiplicity, shape and attractivity of the  heterogeneous steady states for the equation.

报告人简介：

易泰山，中山大学数学学院(珠海)教授、博士生导师。1999年和2004 年分别获湖南大学应用数学学士学位和博士学位。2006年9月至2008年8月先后在加拿大西安大略大学、劳瑞尔大学及约克大学做博士后。2005起先后在湖南大学、中南大学、中山大学任教，现为中山大学数学学院(珠海)教授、博士生导师。主要从事泛函微分方程、反应扩散方程、动力系统及其应用方面的研究，已在SIAM Journal on Mathematical Analysis、Journal of Differential Equations、Proc. R. Soc.Lond. Ser. A、J. Dynam. Differential Equations等国际著名刊物发表论文三十余篇。主持了3 项国家自然科学基金项目和1项湖南省杰出青年基金，2008年入选教育部新世纪优秀人才支持计划。