关于举行上海师范大学王荣年教授学术报告会的通知

报告题目：Theory of Invariant Manifolds for Infinite-dimensional Nonautonomous Dynamical Systems and Applications

报 告人：王荣年 教授（上海师范大学）

报告时间：2022年3月21日（星期一）上午10:00-- 11:00             

报告地点：腾讯会议：215 773 446，密码：220321

邀 请人：曾才斌 副教授

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数学学院

2022年3月18日

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.

报告人简介：王荣年, 博士, 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的适定性、多值扰动及解集的拓扑正则性、不变流形理论等问题的研究, 完成的研究结果已被Mathematische Annalen、International Mathematics Research Notices、Journal of Functional Analysis、Journal of Differential Equations、Journal of Physics A: Mathematical and Theoretical.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。