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ISSN 1079-6762

 

Global weak solutions of non-isothermal front propagation problem


Authors: Bo Su and Martin Burger
Journal: Electron. Res. Announc. Amer. Math. Soc. 13 (2007), 46-52
MSC (2000): Primary 70H20, 35R35, 35L45
Published electronically: May 14, 2007
MathSciNet review: 2320681
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Abstract: We show the global existence of weak solutions for a free-boundary problem arising in the non-isothermal crystallization of polymers. In particular, the free interface is shown to be of codimension one for every time $ t$ in two space dimensions; Hölder continuity of the temperature $ u$ is proven.


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Additional Information

Bo Su
Affiliation: Department of Mathematics, Iowa State University, Ames, Iowa 50011
Email: bosu@iastate.edu

Martin Burger
Affiliation: Industrial Mathematics Institute, Johannes Kepler University, Altenbergerstr. 69, A 4040 Linz, Austria
Email: martin.burger@jku.at

DOI: http://dx.doi.org/10.1090/S1079-6762-07-00173-4
PII: S 1079-6762(07)00173-4
Keywords: Free boundary, level-set method, heat conduction, growth, crystallization, Hausdorff measure, codimension-one-measure estimate, decomposition
Received by editor(s): September 15, 2006
Published electronically: May 14, 2007
Communicated by: Luis A. Caffarelli
Article copyright: © Copyright 2007 American Mathematical Society