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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Homogenization of one-phase Stefan-type problems in periodic and random media


Authors: Inwon C. Kim and Antoine Mellet
Journal: Trans. Amer. Math. Soc. 362 (2010), 4161-4190
MSC (2010): Primary 35Q35, 35Q80, 74Q10, 78M40
Published electronically: March 24, 2010
MathSciNet review: 2608400
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Abstract: We investigate the homogenization of Stefan-type problems with oscillating diffusion coefficients. Both cases of periodic and random (stationary ergodic) mediums are considered. The proof relies on the coincidence of viscosity solutions and weak solutions (which are the time derivatives of the solutions of an obstacle problem) for the Stefan problem. This coincidence result is of independent interest.


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Additional Information

Inwon C. Kim
Affiliation: Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095

Antoine Mellet
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742

DOI: http://dx.doi.org/10.1090/S0002-9947-10-04945-7
PII: S 0002-9947(10)04945-7
Received by editor(s): February 25, 2008
Published electronically: March 24, 2010
Additional Notes: The first author was partially supported by NSF-DMS 0700732
The second author was partially supported by NSF grant DMS-0456647.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.