报告题目：Convergence of Solutions of Parabolic Allen-Cahn equations to Brakke's flow

报 告 人：郑高峰 教授 华中师范大学

报告时间：2021年5月15日 10:10

报告地点：澳门永利官网总站入口老网址三楼天元东北中心第三研讨室

校内联系人：张凯 zhangkaimath@jlu.edu.cn

报告摘要：In this talk, we study the parabolic Allen–Cahn equation, which has slow diffusion and fast reaction, with a potential K. In particular, the convergence of solutions to a generalized Brakke’s mean curvature flow is established in the limit of a small parameter ε → 0. More precisely, we show that a sequence of Radon measures, associated to energy density of solutions to the parabolic Allen–Cahn equation, converges to a weight measure of an integral varifold. Moreover, the limiting varifold evolves by a vector which is the difference between the mean curvature vector and the normal part of ∇ K /2 K. We also discuss the similar situation for Dirichlet boundary value problem.

报告人简介：郑高峰，华中师范大学数学与统计学学院副经理，教授、博士生导师。主要从事偏微分方程和几何发展方程的研究。曾主持国家自然科学基金项目四项，在JFA, Calculus of Variation and PDEs, Ann. I. H. Poincare-AN, JDE等杂志上发表论文二十余篇。曾作为主要参与人获得国家高等学校教学成果奖二等奖一项，湖北省高等学校教学成果奖一等奖两项。曾作为洪堡学者在德国柏林自由大学访问，在美国普渡大学，中佛罗里达大学访问。