报 告 人：王荣年 教授（上海师范大学）
报告题目：Theory of Invariant Manifolds for Infinite-dimensional Nonautonomous Dynamical Systems and Applications
报告时间：2021年05月24日（周一）下午17:00-18:00
报告地点：9#1508
主办单位：数学与统计学院、科学技术研究院
报告人简介：
王荣年,上海师范大学教授, 博士生导师（应用数学）。目前主要从事非线性发展方程适定性、多值扰动及解集的拓扑正则性、动力系统的不变流形理论等问题的研究, 完成的研究结果已被Math. Annalen、Journal of Functional Analysis、Journal of Differential Equations、J. Phys. A: Math. Theo.等学术期刊发表。主持承担了2项国家自然科学基金面上项目、国家自然科学基金青年项目、4项省自然科学基金项目和2项省教育厅基金项目。
报告摘要：
We consider an abstract nonautonomous dynamical system defined on a general Banach space. We prove that under several conditions, there exists a finite-dimensional Lipschitz invariant manifold. The manifold has an exponential tracking property acting on a local range. We then apply this general framework to two types of nonautonomous evolution equations: Scalar reaction-diffusion equations and FitzHugh-Nagumo systems, on 2-D rectangular domains or a 3-D cubic domain. We prove the existence of an inertial manifold of nonautonomous type for the former while a finite-dimensional global manifold for the latter. It is significant that the spectrum of the Laplacian $\Delta$ is not guaranteed to have arbitrarily large gaps on these spatial domains.
邀请人：杜增吉教授