卓越大讲堂 报告题目: Theory of Invariant Manifolds for Infinite-dimensional Nonautonomous Dynamical Systems and Applications 报告人:王荣年上海师范大学教授 报告时间:2022年11月8日11:00-12:00 报告地点:腾讯会议： 584603906
报告摘要：We consider an abstract nonautonomous dynamical system defined on a general Banach space. We prove that if a geometrical assumption, called local strong squeezing property, and several technical assumptions, called controllability, inverse Lipschitz, and (partial) compactness property, are satisfied, then the system admits a finite-dimensional Lipschitz invariant manifold with an exponential tracking property acting on a local range. We then apply this general framework to two types of nonautonomous evolution equations: Reaction-diffusion equations and FitzHugh-Nagumo systems, driven by time-dependent additive/multiplicative forces, on a 2-D rectangular domain or a 3-D cubic domain. It issignificant that on the 3D domain the spectrum of the linear unbounded operator in the principal part does not have arbitrarily large gaps.We prove the existence of an inertial manifold of nonautonomous type for the former while a finite-dimensional global manifold for the latter. Each manifold controls the long-time behavior of solutions of the corresponding system.
专家简历：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、不变测度等问题的研究,完成的研究结果已被Mathematische Annalen、“Int Math Res Notices”、“SIAM Journal on Applied Dynamical Systems”、“Journal of Functional Analysis”、“Journal of Differential Equations”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。曾获聘广东省高等学校省级培养对象等。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。
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