Singular Limit Problem for the Allen-Cahn Equation with a Zero Neumann Boundary Condition on Non-Convex Domains
Host
Department of Applied Mathematics
Speaker
Takashi Kagaya
Division of Fundamental mathematics, Institute of Mathematics for Industry, Kyushu University
https://kyushu-u.pure.elsevier.com/en/persons/takashi-kagaya
Description
We consider the flow of hyper-surface generating 90 degree contact angle on the boundary of a bounded domain. The motion is governed by the mean curvature flow equation. For this free boundary problem, the mean curvature flow should "pop" upon tangential contact with the boundary of the domain. Therefore, we prove the global existence of Brakke's mean curvature flow with free boundary via a singular limit problem for the Allen-Cahn equation with a zero Neumann boundary condition.
Event Topic
Stochastic & Multiscale Modeling and Computation