The area-preserving anisotropic motion of a phase interface arising from Allen-Cahn equation
Xiao-Liu Wang, Yaping Wang · Discrete and Continuous Dynamical Systems · 2025
In this paper, we study an area-preserving anisotropic curvature flow in the plane which describes the motion of phase interface arising form the nonlocal anisotropic Allen-Cahn equation, and show that for any convex initial curve, the evolving curves converge to the boundary of the Wulff shape defined by an anisotropic function as time goes to infinity.