Liquid Flow in Partially Saturated Porous Media

Abstract

We consider a picture for the filtration of a liquid in a partially saturated porous medium, leading to a two-phase one-dimensional free boundary problem of the following type: The liquid pressure satisfies an elliptic equation in the saturated region and a non-linear parabolic equation in the unsaturated region, while pressure and velocity are continuous across the interface. This scheme reduces to the study of the non-linear parabolic free boundary problem in the unsaturated phase with cauchy data prescribed on the free boundary, for such a problem existence, uniqueness and continuous dependence theorems are proved.