亚博体彩到账快的

亚博体彩到账快的

2021年信息与数学亚博体彩到账快的学术报告(十三)

讲座题目Theory of Invariant Manifolds for Infinite-dimensional Nonautonomous Dynamical Systems and Applications

主办单位:长江大学信息与数学亚博体彩到账快的

报告专家:王荣年(上海师范大学 教授)

报告时间2021630(周三) 15:00-16:00

报告地点东校区8-406

专家简介王荣年, 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 AnnalenInternational Mathematics Research NoticesJournal 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. 曾获聘广东省高等亚博体彩到账快的“千百十人才工程”省级培养对象、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亚博体彩到账快的和雅西大学、奥地利克拉根福特大学、美国杨百翰大学和佐治亚理工亚博体彩到账快的等。

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.

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