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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