A free boundary problem for a fluid flow in a heterogeneous porous medium

Abstract

In this paper we study the problem of seepage of a fluid through a porous medium, assuming the flow governed by a nonlinear Darcy law and nonlinear leaky boundary conditions. We prove the continuity of the free boundary and the existence and uniqueness of minimal and maximal solutions. We also prove the uniqueness of the S3-connected solution in various situations. © 2003 Università degli Studi di Ferrara.