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

Blank, Ivan; Korten, Marianne; Moore, Charles

doi:10.1090/S0002-9947-08-04764-8

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.

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