Optimal relaxation to a planar interface in the Mullins-Sekerka problem
Analysis of PDEs
2018-06-07 v3
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.
Keywords
Cite
@article{arxiv.1709.04833,
title = {Optimal relaxation to a planar interface in the Mullins-Sekerka problem},
author = {Olga Chugreeva and Felix Otto and Maria G. Westdickenberg},
journal= {arXiv preprint arXiv:1709.04833},
year = {2018}
}