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报告室

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。