Penetration of a wetting front in a porous medium interacting with the flow (Q1363132)

This paper deals with a one-dimensional filtration problem describing the flow of an incomprehensible fluid injected in a dry solid at a given pressure. The model considers a porous medium. Capillarity is neglected and the penetrating fluid creates a wetting front which separates the dry soil from the saturated medium. The governing equations are partial differential equations with initial and boundary conditions. The aim of the paper is to obtain the global existence and uniqueness of a classical solution under some reasonable hypothesis. The authors do not give numerical examples.