WIAS Preprint No. 1567, (2010)

The degenerate and non-degenerate Stefan problem with inhomogeneous and anisotropic Gibbs--Thomson law



Authors

  • Kraus, Christiane

2010 Mathematics Subject Classification

  • 49Q20 82B26 58B20 80A22

Keywords

  • Stefan problems, phase transitions, Gibbs-Thomson law, free boundaries, variational problems, geometric measure-theory

Abstract

The Stefan problem is coupled with a spatially inhomogeneous and anisotropic Gibbs-Thomson condition at the phase boundary. We show the long-time existence of weak solutions for the non-degenerate Stefan problem with a spatially inhomogeneous and anisotropic Gibbs-Thomson law and a conditional existence result for the corresponding degenerate Stefan problem. To this end approximate solutions are constructed by means of variational functionals with spatially inhomogeneous and anisotropic interfacial energy. By passing to the limit, we establish solutions of the Stefan problem with a spatially inhomogeneous and anisotropic Gibbs-Thomson law in a weak generalized BV-formulation.

Appeared in

  • European J. Appl. Math., 22 (2011) pp. 393--422.

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