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

Garcke, Harald and Schaubeck, Stefan (2011) Existence of weak solutions for the Stefan problem with anisotropic Gibbs-Thomson law. Preprintreihe der Fakultät Mathematik 16/2011, Working Paper. (Unpublished)

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Abstract

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.

Item Type:Monograph (Working Paper)
Institutions: Mathematics > Prof. Dr. Harald Garcke
Classification:
NotationType
35K55MSC
35R35MSC
49Q20MSC
73B40MSC
82B26MSC
58B20MSC
80A22MSC
Keywords:Stefan problem, anisotropy, Gibbs-Thomson law, free boundary, implicit time discretization
Subjects:500 Science > 510 Mathematics
Status:Unpublished
Refereed:No, this version has not been refereed yet (as with preprints)
Created at the University of Regensburg:Yes
Owner:Eva Ruetz
Deposited On:18 Apr 2011 08:29
Last Modified:06 Sep 2011 09:04
Item ID:20519
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