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DiBenedetto, Emmanuele; Friedman, Avner

Conduction-convection problems with change of phase. (English) Zbl 0593.35085

J. Differ. Equations 62, 129-185 (1986).
In the usual simplest formulation of free boundary problems one considers only the conduction, here a formulation is studied where also convective motions are taking into account. Two problems are studied: a ground freezing one, in which the water is subjected to Darcy’s law, and a two phases stationary Stefan problem, where the motion of water is governed by the Navier-Stokes equations. Results on regularity of the solutions and of the free boundary are given in both cases.
Reviewer: M.Biroli

Cited in 13 Documents

MSC:

35R35 Free boundary problems for PDEs
35B65 Smoothness and regularity of solutions to PDEs
35Q30 Navier-Stokes equations
76R99 Diffusion and convection
80A20 Heat and mass transfer, heat flow (MSC2010)

Keywords:

free boundary problems; convective motions; Darcy’s law; Stefan problem; Navier-Stokes equations; regularity of the solutions
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\textit{E. DiBenedetto} and \textit{A. Friedman}, J. Differ. Equations 62, 129--185 (1986; Zbl 0593.35085)
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