中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人：周恒宇 教授（重庆大学）   
题  目：The Dirichlet problem of prescribed mean curvature equations via blow ups, I: monotone cases
时  间：2022.05.25（星期三）上午9:00-10:00
地  点：腾讯会议  948-3602-5762
摘  要：This is the first one of our series of papers to study the Dirichlet problem of prescribed mean curvature equations via a blowup technique inspired from Shoen-Yau’s proof on the positive mass theorem. These equations includes Jang equations and minimal surface equations in warped product manifolds. We relate the solvability of these Dirichlet problems with a toplogical condition (NCf-condition) from the prescribed mean curvature functions. A key ingredient of our proof are an extension of curvature estimates of C^2 almost minimal boundaries from Simon’s idea.
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报告人：袁旭 教授（香港中文大学）   
题  目：Global behavior of small data solutions for the 2D Dirac--Klein-Gordon equations
时  间：2022.05.26（星期四）上午10:00-11:00
地  点：腾讯会议 585-235-442
摘  要：The Dirac--Klein-Gordon system is a basic model in particle physics, describing a scalar field and a Dirac field through Yukawa interactions. In this talk, we discuss the two-dimensional Dirac--Klein-Gordon system with a massive scalar field and a massless Dirac field. We will present the recent result of the global behaviors of small data solutions to this system. The main ingredients in our proof are the vector field method and the Ghost weight energy estimate. Our result is valid for general small, high-regular initial data, in particular, there is no restriction on the support of the initial data. This talk is based on the joint work with Shijie Dong, Kuijie Li and Yue Ma.