The Hele-Shaw problem as a “Mesa” limit of Stefan problems: Existence, uniqueness, and regularity of the free boundary
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- by Ivan A. Blank, Marianne K. Korten and Charles N. Moore PDF
- Trans. Amer. Math. Soc. 361 (2009), 1241-1268 Request permission
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.References
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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
- Received by editor(s): October 18, 2006
- Published electronically: October 10, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 1241-1268
- MSC (2000): Primary 76D27, 35K65, 49J40
- DOI: https://doi.org/10.1090/S0002-9947-08-04764-8
- MathSciNet review: 2457397