Optimal relaxation to a planar interface in the Mullins-Sekerka problem

2017/09/14 by Olga Chugreeva, Chugreeva, Olga, Félix Otto +4
Computer Science · Materials Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Solidification and crystal growth phenomena #math.AP

paper · pdf · doi:10.48550/arxiv.1709.04833

arxiv created 2018/06/06 · arxiv updated 2018/06/07

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.

Related

• Sharp Convergence to the Half-Space for Mullins-Sekerka in the Plane
• Convergence to the planar interface for a nonlocal free-boundary evolution
• Relaxation of perturbed circles in flat spaces for the Mullins-Sekerka evolution in two dimensions
• Optimal L¹-type relaxation rates for the Cahn-Hilliard equation on the line
• Mullins-Sekerka as the Wasserstein flow of the perimeter