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Modelling of interfaces in unsaturated porous media. (English) Zbl 1163.76417

Summary: In this contribution we discuss interface conditions for unsaturated flow in porous media. Our aim is to provide a concise collection of the arguments that lead to the standard models for interfaces that either separate two porous media or a porous medium and void space. We furthermore present a regularization procedure for these interface conditions. In a singular limit, a nonlinear boundary condition of third kind can provide approximate solutions to the outflow condition of Signorini type.

MSC:

76S05 Flows in porous media; filtration; seepage
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35K65 Degenerate parabolic equations
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