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A degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions. (English) Zbl 1116.35073

Summary: We prove existence and uniqueness of weak solutions for a general degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions. Particular instances of this problem appear in various phenomena with changes of phase like the multiphase Stefan problem and in the weak formulation of the mathematical model of the so-called Hele-Shaw problem. Also, the problem with nonhomogeneous Neumann boundary conditions is included.

MSC:

35K65 Degenerate parabolic equations
35M10 PDEs of mixed type
35R35 Free boundary problems for PDEs
35J60 Nonlinear elliptic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
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