报告题目：Theory and Applications of Equivariant Normal Forms and Hopf bifurcation for Semilinear FDEs in Banach Spaces

报告时间：2022年3月 31 日上午10:00-12:30

报告地点：腾讯会议（ID:260-388-676）

报告专家：郭上江教授

主办单位：三峡数学研究中心/湖北省数学与交叉科学创新引智基地

专家简介：郭上江，中国地质大学(武汉)二级教授、博士生导师、数理学院院长，湖南大学岳麓学者特聘A岗教授、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。2014-2019来连续入选“中国高被引学者”榜单。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)。担任包含国际SCI刊物《Bulletin of the Malaysian Mathematical Sciences Society》在内的4个学术刊物的编委。

报告摘要：This paper is concerned with equivariant normal forms of semilinear functional differential equations (FDEs) in general Banach spaces. The analysis is based on the theory previously developed for autonomous delay differential equations and on the existence of invariant manifolds. As an important application of equivariant normal forms, we not only establish equivariant Hopf bifurcation theorem for semilinear FDEs in general Banach spaces, but also in a natural way derive criteria for the existence, stability, and bifurcation direction of branches of bifurcating periodic solutions. We employ these general results to obtain the existence of infinite many small-amplitude wave solutions for a delayed Ginzburg-Landau equation on a two-dimensional disk with the homogeneous Dirichlet boundary condition.