Penetration of a wetting front in a porous medium interacting with the flow

In this paper the authors analyze a model for the wetting of a porous medium by flow of water from above with the extra feature that the medium deforms as it absorbs water, and hence its porosity changes. The model consists of a coupled system of three first-order equations for the pressure, flux and porosity. Existence and uniqueness are shown, and examples where non-uniqueness is possible are also mentioned. The paper, and in particular the model, should be of interest to researchers working on models of rain uptake by soil and similar problems