Quasi-static evolution of polyhedral crystals

Przemysław Górka

doi:10.3934/dcdsb.2008.9.309

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2008, Volume 9, Issue 2: 309-320. Doi: 10.3934/dcdsb.2008.9.309

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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

Received: January 31, 2007

Revised: September 30, 2007

Published: February 2008

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Abstract

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:

Free boundary problem; crystal growth; Gibbs-Thomson relation,
Stefan problem.

Mathematics Subject Classification: Primary: 35R35 ; Secondary: 53C44.

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