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March  2008, 9(2): 309-320. doi: 10.3934/dcdsb.2008.9.309

Quasi-static evolution of polyhedral crystals

Przemysław Górka 1,

1. 

Department of Mathematics and Information Sciences, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland

Received  February 2007 Revised  October 2007 Published  December 2007

We examine quasi-static evolution of crystals in three dimensions. We assume that the Wulff shape is a prism with a hexagonal base. We include the Gibbs-Thomson law on the crystal surface and the so-called Stefan condition. We show local in time existence of solutions assuming that the initial crystal has admissible shape.
Keywords: Stefan problem., Free boundary problem; crystal growth; Gibbs-Thomson relation.
Mathematics Subject Classification: Primary: 35R35 ; Secondary: 53C4.
Citation: Przemysław Górka. Quasi-static evolution of polyhedral crystals. Discrete & Continuous Dynamical Systems - B, 2008, 9 (2) : 309-320. doi: 10.3934/dcdsb.2008.9.309
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