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

DiBenedetto, Emmanuele; Friedman, Avner

doi:10.1090/S0002-9947-1984-0728709-6

The ill-posed Hele-Shaw model and the Stefan problem for supercooled water
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by Emmanuele DiBenedetto and Avner Friedman PDF

Trans. Amer. Math. Soc. 282 (1984), 183-204 Request permission

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 $G$. 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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