报告一：Invariant Manifolds of the Phase-field Systems

报告二：3-D Nonlinear Hyperbolic-parabolic Problems: Invariant Manifolds

报告三：Topological Regularity of the Solution Sets for Multivalued Nonlinear Evolution Equations

报告人：  王荣年 教授  上海师范大学

时 间：2020年12月10日8:00-8:50，9:00-9:50，10:00-10:50  

地 点： 腾讯会议ID：302 786 507

报告一摘要：In this talk we review the theory of invariant manifolds for a phase-field system in higher space dimensions. Assuming the strong dissipation, we prove that the system, equipped boundary conditions of the Dirichlet type, has a global finite-dimensional manifold.

报告二摘要：In this talk we investigate the existence of invariant manifolds for a coupled problem of nonlinear hyperbolic-parabolic PDEs in 3-D torus. The problem arises usually in the study of wave propagation phenomena with viscous damping which are heat generating. The spectral gap condition already fails for it.  We prove that the dynamical system determined by it possesses a Lipschitz manifold which is locally invariant under the semiflow. The locally asymptotic stability and regularity of the manifold are also considered. Moreover, under more assumptions, it is proved that the manifold is provided with the feature as that global manifold usually holds. Through it all, no large damping and heat diffusivity are needed.

报告三摘要：In this talk we consider the Cauchy problems of multivalued nonlinear evolution equations. Main attention is paid to settling their solution sets carrying Aronszajn-type topological regularity.

个人简介：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。完成的研究结果已在“Math. Annalen”、“Journal of Functional Analysis”、“Journal of Differential Equations”、“J. Phys. A: Math. Theo.”等学术期刊发表。主持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。 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。