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A free boundary problem describing the saturated-unsaturated flow in a porous medium. II: Existence of the free boundary in the 3D case. (English) Zbl 1105.35148

The author studies a 3D flow problem in an isotropic homogeneous porous medium with capillarity under gravity. The medium is bounded between two horizontal planes. On the top surface the total flux is prescribed, while the bottom and the lateral boundary are considered to be semipermeable. The problem is referred to rain water infiltration, although in this case flux may not be prescribed at all times at the inflow surface. A sequence of approximating solutions is introduced which are shown to be vertically monotone (so that the saturation surface is defined) and which converge to the desired solution. In the latter, when saturation occurs the unsaturated region lies above the saturated region (thus the flux imposed may not be interpreted as due to rain fall, but it may require a mechanical action to be enforced). Uniqueness is also proved.

MSC:

35R35 Free boundary problems for PDEs
76S05 Flows in porous media; filtration; seepage
35K35 Initial-boundary value problems for higher-order parabolic equations

Citations:

Zbl 1133.76350
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