Electron. J. Diff. Eqns., Vol. 2002(2002), No. 73, pp. 1-21.

A coupled Cahn-Hilliard particle system

Tony Shardlow

A Cahn-Hilliard equation is coupled to a system of stochastic differential equations to model a random growth process. We show the model is well posed and analyze the model asymptotically (in the limit of the interfacial distance becoming small), to recover a free boundary problem. A numerical method together with example solutions is presented.

Submitted April 5, 2002. Published August 13, 2002.
Math Subject Classifications: 35K35, 65M60, 60H15.
Key Words: Boundary Value Problems, Finite Element Methods, Stochastic Partial Differential Equations.

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Tony Shardlow
Department of Mathematical Sciences,
Science Laboratories, South Road,
Durham University, Durham DH1 3LE, UK
e-mail: Tony.Shardlow@durham.ac.uk
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