Relaxation to a planar interface in the Mullins–Sekerka problem

  • Olga Chugreeva

    RWTH Aachen, Germany
  • Felix Otto

    Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany
  • Maria G. Westdickenberg

    RWTH Aachen, Germany
Relaxation to a planar interface in the Mullins–Sekerka problem cover
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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.

Cite this article

Olga Chugreeva, Felix Otto, Maria G. Westdickenberg, Relaxation to a planar interface in the Mullins–Sekerka problem. Interfaces Free Bound. 21 (2019), no. 1, pp. 21–40

DOI 10.4171/IFB/415