In this paper 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 multiphase Stefan problem and in the weak formulation of the mathematical model of the so called Hele Shaw problem. Also, the problem with non-homogeneous Neumann boundary condition is included.
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Fuensanta Andreu, José M. Mazón, Julián Toledo, N. Igbida, A degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions. Interfaces Free Bound. 8 (2006), no. 4, pp. 447–479DOI 10.4171/IFB/151