A One-dimensional Flow Problem in Porous Media with Hydrophile Grains

摘要

We study a free boundary problem describing the propagation of the wetting front following the injection of a liquid into a porous medium with hydrophile granules. The absorption process produces a non-local interaction with the flow so that the porosity appearing in the parabolic equation for pressure is a functional of saturation and of the free boundary. Our analysis is confined to the unsaturated regime, which is the first stage of the process. An existence theorem is proved.