报 告 人：郑高峰 教授（华中师范大学）

报告时间：2019年12月30号 14:30

报告地点：数学实验室

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院长，教授。博士毕业于香港中文大学数学系。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。