报告题目：Invariant manifolds of the generalized phase-field systems

报 告 人：王荣年 教授 上海师范大学

照    片：

邀 请 人：吴事良 常永奎

报告时间：2020年9月11日（周五） 16：00-17：00

报告平台：腾讯会议ID： 309140985

报告人简介：王荣年教授博士毕业于中国科学技术大学基础数学专业。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``Math. 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. 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、杨百翰大学、佐治亚理工学院等。

报告摘要：In this talk we review the theory of invariant manifolds for a phase-field system in higher space dimensions. As a starting point, we consider an infinite-dimensional dynamical system generated by the coupled problem of nonlinear evolution equations in Hilbert spaces. The linear parts of these two equations differ essentially in both spectrum and regularity. We prove the existence of an invariant manifold for the dynamical system without assuming any spectral gap condition. Then, considering the generalized phase-field system on the rectangle or cube domains, we obtain a finite-dimensional local manifold, where homogeneous boundary conditions of the Dirichlet type are imposed. This manifold, which attracts exponentially only regular enough solutions, is locally invariant under the semiflow. The map constructing it has a compact support. If more assumptions are made, we prove that the manifold would contain the global attractor as supposed to.