No. 2019.02
Relaxation to a planar interface in the Mullins-Sekerka problem
O. Chugreeva, F. Otto, and M. G. Westdickenberg
Subject: Mullins-Sekerka, energy method, relaxation rates, planar profile


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.


Interfaces Free Bound. 21 (2019), no. 1, 21–40