A One-dimensional flow problem in porous media with hydrophile grains
Antonio Fasano · Mathematical Methods in the Applied Sciences · 1999
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. Copyright © 1999 John Wiley & Sons, Ltd.