Relaxation to a planar interface in the Mullins–Sekerka problem

Abstract

We analyze the convergence rates to a planar interface in the Mullins–Sekerka model by applying a relaxation method based on relationships among distance, energy, and dissipation. The relaxation method was developed by two of the authors in the context of the 1-d Cahn–Hilliard equation and the current work represents an extension to a higher dimensional problem in which the curvature of the interface plays an important role. The convergence rates obtained are optimal given the assumptions on the initial data.