Convergence of the Allen-Cahn equation with Neumann boundary condition on non-convex domains

Takashi Kagaya

Published 2017-10-02Version 1

We study a singular limit problem of the Allen-Cahn equation with the homogeneous Neumann boundary condition on non-convex domains with smooth boundaries under suitable assumptions for initial data. The main result is the convergence of the time parametrized family of the diffused surface energy to Brakke's mean curvature flow with a generalized right angle condition on the boundary of the domain.