Electron. J. Diff. Eqns. Vol. 1995(1995), No. 11, pp. 1-28.

A numerical scheme for the two phase Mullins-Sekerka problem

Peter W. Bates, Xinfu Chen, & Xinyu Deng

Abstract:
An algorithm is presented to numerically treat a free boundary problem arising in the theory of phase transition. The problem is one in which a collection of simple closed curves (particles) evolves in such a way that the enclosed area remains constant while the total arclength decreases. Material is transported between particles and within particles by diffusion, driven by curvature which expresses the effect of surface tension. The algorithm is based on a reformulation of the problem, using boundary integrals, which is then discretized and cast as a semi-implicit scheme. This scheme is implemented with a variety of configurations of initial curves showing that convexity or even topological type may not be preserved.

This article includes an erratum attached on September 26, 1995.

Submitted June 14, 1995. Published August 18, 1995.
Math Subject Classification: 35R35, 65C20, 65M06, 65R20, 82C26.
Key Words: Boundary Integral, Free Boundary Problem, Motion by Curvature, Ostwald Ripening

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Peter W. Bates (peter@math.byu.edu)
Xinyu Deng (cindy@math.byu.edu)
Mathematics, Brigham Young University, Provo, UT 84602, USA

Xinfu Chen
Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA
e-mail: xinfu+@pitt.edu

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