Regularization of outflow problems in unsaturated porous media with dry regions

We study a porous medium with saturated, unsaturated, and dry regions, described by Richards' equation -for the saturation s and the pressure p. Due to a degenerate permeability coefficient k(x, s) and a degenerate capillary pressure function pc(x, s), the equations may be of elliptic, parabolic, or of ODE-type. We construct a parabolic regularization of the equations and find conditions that auarantee the convergence of the parabolic solutions to a solution of the degenerate system. An example shows that the convergence fails in general. Our approach provides an existence result for the outflow problem in the case of x-dependent coefficients and a method for a numerical approximation. (c) 2007 Published by Elsevier Inc.