2018年信息与数学学院学术报告(三十一)

讲座题目: Convergence of solutions of the weighted Allen-Cahn equations to Brakke flow.(关于加权Allen-Cahn方程的解趋向于Brakke流时的收敛性)

主办单位:长江大学信息与数学学院

报告专家:郑高峰(华中师范大学,教授,博导)

报告时间:2018125日 周五下午:16:00-1730

报告地点:东校区8-406

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专家简介:郑高峰,华中师范大学数学与统计学学院教授,博士生导师。2005年博士毕业于香港中文大学数学系。曾主持国家自然科学基金面上项目2项,青年基金1项以及教育部归国留学基金1项。在JFA, CVPDE, AIH Poincare等期刊上发表十余篇学术论文。

摘要:This talk concerns the parabolic Allen-Cahn equation with a potential function  with slow diffusion and fast reaction. In particular, the convergence of solutions to a generalized Brakke's mean curvature flow is established as a small parameter . 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 .

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