Regularization in phase transitions with Gibbs-Thomson law

Description

We study the regularity of weak solutions for the Stefan and Hele- Shaw problems with Gibbs-Thomson law under special conditions. The main result says that whenever the free boundary is Lipschitz in space and time it becomes (instantaneously) C[superscript 2,alpha] in space and its mean curvature is Hölder continuous. Additionally, a similar model related to the Signorini problem is introduced, in this case it is shown that for large times weak solutions converge to a stationary configuration. / text

Links & Downloads

1. http://hdl.handle.net/2152/ETD-UT-2010-12-2562

Tags

Nonlinear partial differential equations

Free boundary problems

Luckhaus theorem

Hele-shaw

Stefan problem

Lipschitz

Almost minimal surfaces

Additional Fields

Identifer	oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/ETD-UT-2010-12-2562
Date	10 February 2011
Creators	Guillen, Nestor Daniel
Source Sets	University of Texas
Language	English
Detected Language	English
Type	thesis
Format	application/pdf