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

 

The Hele-Shaw problem as a ``Mesa'' limit of Stefan problems: Existence, uniqueness, and regularity of the free boundary


Authors: Ivan A. Blank, Marianne K. Korten and Charles N. Moore
Journal: Trans. Amer. Math. Soc. 361 (2009), 1241-1268
MSC (2000): Primary 76D27, 35K65, 49J40
Published electronically: October 10, 2008
MathSciNet review: 2457397
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Abstract: We study a Hele-Shaw problem with a mushy region obtained as a mesa type limit of one-phase Stefan problems in exterior domains. We deal with both Neumann and Dirichlet data and show pointwise convergence of the Stefan solutions to the Hele-Shaw solution. We make no assumptions on the geometry, topology, or connectivity of the injection slot.


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Additional Information

Ivan A. Blank
Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
Email: blanki@math.ksu.edu

Marianne K. Korten
Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
Email: marianne@math.ksu.edu

Charles N. Moore
Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
Email: cnmoore@math.ksu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04764-8
PII: S 0002-9947(08)04764-8
Keywords: Mesa problem, Hele-Shaw problem, Stefan problem, free boundary, mushy region, singular limit
Received by editor(s): October 18, 2006
Published electronically: October 10, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.