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

1984; American Mathematical Society; Volume: 282; Issue: 1 Linguagem: Inglês

10.1090/s0002-9947-1984-0728709-6

1088-6850

Emmanuele DiBenedetto, Avner Friedman,

Advanced Mathematical Modeling in Engineering

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 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.