報告題目：Convergence of Solutions of Parabolic Allen-Cahn equations to Brakke's flow
報 告 人：鄭高峰 教授 華中師範大學
報告時間：2021年5月15日 10:10
報告地點：伟德线上平台三樓天元東北中心第三研讨室
校内聯系人：張凱 zhangkaimath@jlu.edu.cn
報告摘要：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.
報告人簡介：鄭高峰，華中師範大學數學與統計學學院副院長，教授、博士生導師。主要從事偏微分方程和幾何發展方程的研究。曾主持國家自然科學基金項目四項，在JFA, Calculus of Variation and PDEs, Ann. I. H. Poincare-AN, JDE等雜志上發表論文二十餘篇。曾作為主要參與人獲得國家高等學校教學成果獎二等獎一項，湖北省高等學校教學成果獎一等獎兩項。曾作為洪堡學者在德國柏林自由大學訪問，在美國普渡大學，中佛羅裡達大學訪問。
