应兰州大学数学与统计学院王智诚教授的邀请，上海师范大学王荣年教授将于2021年11月27日-11月28日与我校有关师生进行在线学术研讨，其中11月27日举行线上专题学术报告。

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

时    间：11月27日10:00

地    点：腾讯会议ID：557250 177

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.

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王荣年教授简介

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"、“Int. Math. Res. Notices 、"Journal of Functional Analysis"、"Journal of Differential Equations"" Journal of 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。

甘肃应用数学中心

甘肃省高校应用数学与复杂系统省级重点实验室

数学与统计学院

萃英学院

2021年11月25日