数学系学术报告
微分方程与动力系统系列报告
报告题目：Theory of Invariant Manifolds for Infinite-dimensional Nonautonomous Dynamical Systems and Applications
报告人：王荣年教授
报告时间：2021/5/25 10:30-11:30
地点：数A302
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、``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、江西省高校中青年骨干教师等。近年来先后访问罗马尼亚科学院和雅西大学、奥地利克拉根福特大学、美国杨百翰大学和佐治亚理工学院等。