Nonstationary filtration in partially saturated porous media

Abstract

Nonstationary two-dimensional filtration in a porous medium is considered, whereby part of the medium is saturated, another part is unsaturated but wet, and the remaining part is dry. The saturated/unsaturated and unsaturated/dry interfaces are free boundaries. It is shown that there exists a unique solution, and that the saturation function is continuous in the wet portion of the medium; this implies that the two interfaces are separated. Under some monotonicity-type conditions on the initial and boundary data it is shown that the free boundaries are continuous.