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Existence of weak solutions for the Stefan problem with anisotropic Gibbs-Thomson law

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Garcke, Harald ; Schaubeck, Stefan
Date of publication of this fulltext: 18 Apr 2011 06:29


The Stefan problem with Gibbs-Thomson law describes solidification phenomena for pure substances. In applications the surface energy is anisotropic leading to an anisotropic Gibbs-Thomson law. We show the existence of weak
solutions to the Stefan problem with anisotropic Gibbs-Thomson law using an implicit time discretization, and variational methods in an anisotropic BV setting. Our main result generalizes an existence result of Luckhaus to the
anisotropic case.

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