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

Andreu, F.; Mazón, J. M.; Toledo, J.; Igbida, N.

Interfaces Free Bound. 8, No. 4, 447-479 (2006).

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)

Keywords:

multiphase Stefan problem; Hele-Shaw problem; nonhomogeneous Neumann boundary conditions