The ill-posed Hele-Shaw model and the Stefan problem for supercooled water

Authors:
Emmanuele DiBenedetto and Avner Friedman

Journal:
Trans. Amer. Math. Soc. **282** (1984), 183-204

MSC:
Primary 35R35; Secondary 35K05, 80A20

DOI:
https://doi.org/10.1090/S0002-9947-1984-0728709-6

MathSciNet review:
728709

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Abstract: The Hele-Shaw flow of a slow viscous fluid between slightly separated plates is analyzed in the ill-posed case when the fluid recedes due to absorption through a core . Necessary and sufficient conditions are given on the initial domain occupied by the fluid to ensure the existence of a solution. Regularity of the free boundary is established in certain rather general cases.

Similar results are obtained for the analogous parabolic version, which models the one-phase Stefan problem for supercooled water.

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DOI:
https://doi.org/10.1090/S0002-9947-1984-0728709-6

Article copyright:
© Copyright 1984
American Mathematical Society