报告题目：Oscillatory and stationary patterns in a diffusive model with delay effect

报 告 人：郭上江 教授

报告时间：2021年5月21日星期五下午4:00-5:40

报告地点：数学楼235

报告摘要：In this talk a reaction-diffusion model with delay effect and Dirichlet boundary condition is considered. Firstly, the existence, multiplicity, and patterns of spatially nonhomogeneous steady-state solution are obtained by using the Lyapunov-Schmidt reduction. Secondly, by means of the space decomposition, we subtly discuss the distribution of eigenvalues of the infinitesimal generator associated with the linearized system at a spatially nonhomogeneous synchronous steady-state solution, and then we derive some sufficient conditions to ensure that the nontrivial synchronous steady-state solution is asymptotically stable. By using the symmetric bifurcation theory of differential equations coupled with representation theory of standard dihedral groups, we not only investigate the effect of time delay on the pattern formation, but also obtain some important results about the spontaneous bifurcation of multiple branches of nonlinear wave solutions and their spatio-temporal patterns.

报告人简介：郭上江，中国地质大学(武汉)二级教授、博士生导师, 湖南大学岳麓学者特聘教授、博士生导师，主要从事微分方程分岔理论及应用研究, 随机动力系统理论及应用研究。主持国家自然科学基金项目6项，在Springer出版社应用数学科学丛书出版了英文专著一部，在JDE, JNS, M3AS, DCDS, ZAMP和Nonlinearity等杂志上发表论文80多篇。获湖南省自然科学奖一等奖(排名第一，2018年),湖南省科技进步一等奖(排名第二，2008年),入选教育部新世纪优秀人才支持计划(2007年）。担任多个国际SCI学术刊物编委。