On Diffusion Induced Segregation in Time-Dependent Domains

Abstract. This article is concerned with the derivation and analysis of a model for diffusion induced segregation phenomena in the physically relevant case that the domain representing the crystal grows in time. A mathematical model is formulated where the phase parameter is a function of bounded variation and the equations are completed with the Gibbs-Thomson law. Based on suitable a-priori bounds, methods from geometric measure theory are applied to derive suitable compactness properties which allow to show the existence of weak solutions in three space dimensions.