Electronic Journal of Differential Equations, 
Vol. 1995(1995), No. 11, pp 1--27. 

Title: A numerical scheme for the two phase Mullins-Sekerka problem

Authors: Peter W. Bates (Brigham Young Univ., Provo, UT, USA)
         Xinfu Chen (Univ. of Pittsburgh, PA, USA)
         Xinyu Deng (Brigham Young Univ., Provo, UT, USA)

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