Sharp interface limit of a matrix-valued Allen-Cahn equation

发布时间：2021-11-10 作者：77779193永利官网浏览次数：

Speaker:	王伟	DateTime:	2021年11月12日（周五）下午3:30-4:30
Brief Introduction to Speaker: 王伟，浙江大学数学科学学院长聘副教授/研究员，2013年博士毕业于北京大学数学科学学院。主要研究领域为应用分析与偏微分方程，包括液晶数学理论，流体自由边值问题等。研究成果在Comm. Pure Appl. Math., Arch. Ration. Mech. Anal, J. Funct. Anal.等期刊发表。		Place:	腾讯会议ID：471 804 642
Abstract:We will talk about the asymptotical behaviour of a matrix-valued Allen-Cahn equation when a small parameter tends to zero. Precisely, we show that the limit system is a two-phases flow system: the phase interface evolves according to the mean curvature flow; in two bulk phase regions, the solution obeys the harmonic map heat flow into two different manifolds; on the interface, the phase matrices in two sides satisfy a novel mixed boundary condition. The proof follow the roadmap developed by de Mottoni-Schatzman and Alikakos-Bates-Chen: we first construct an approximate solution solving the regularized system up to arbitrary small terms, and then we prove a spectral lower bound for the linearized operator around it, and finally we estimate the difference between the true solution and the approximate solution. The main difficulties come from the inherent (partially minimal pairing) property of this problem.