Lecturer: Fei Mingwen

Abstract:

In this talk we consider the sharp interface limit of a matrix-valued Allen-Cahn equation. 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.

Introduction to the Lecturer:

Fei Mingwen, professor and doctoral supervisor from School of Mathematics & Statistics, Anhui Normal University, is mainly engaged in the research on incompressible fluid equation, and has made important breakthroughs in sharp interface limit in the fluid and liquid crystal field.

Invited by:

Tao Tao, Professor from School of Mathematics

Time:

10:00-11:00, September 9 (Thursday)

Venue:

Tencent Meeting, Meeting ID: 427 916 397

Hosted by: School of Mathematics, Shandong University