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

Published online by Cambridge University Press:  30 March 2011

CHRISTIANE KRAUS
CHRISTIANE KRAUS*
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany email: [email protected]
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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 problems for energy 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 generalised BV-formulation.

Keywords

Stefan problemPhase transitionsGibbs–Thomson lawFree boundariesVariational problemsGeometric measure-theory
Type
Papers
Information
European Journal of Applied Mathematics , Volume 22 , Issue 5 , October 2011 , pp. 393 - 422
Copyright
Copyright © Cambridge University Press 2011

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