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

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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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