学术报告(费明稳 3.18)

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

发布人:肖怡霏 发布日期:2022-03-09
主题
Sharp interface limit of a matrix-valued Allen-Cahn equation
活动时间
-
活动地址
腾讯会议 会议ID: 642 711 460
主讲人
费明稳 教授 安徽师范大学
主持人
黄景炽

In this talk we consider the singular asymptotic limit of a diffuse interface model for a matrix-valued Allen-Cahn equation, when a parameter $\varepsilon>0$ that is proportional to the thickness of the diffuse interface tends to zero. We show that the sharp interface limit system is a two-phases flow system: the interface evolves according to the motion by mean curvature; in the two bulk phase regions, the solution obeys the heat flow of harmonic maps with values in the sets of nˆn orthogonal matrices with determinant 1 and -1 respectively; on the interface, the phase matrices in two sides satisfy a novel mixed boundary condition. The above result provides a solution to the Keller-Rubinstein-Sternberg's (conjecture) problem in the orthogonal matrix setting. This is a joint work with Prof. Fanghua Lin, Prof. Wei Wang and Prof. Zhifei Zhang.