JournalsifbVol. 6 , No. 1DOI 10.4171/ifb/91

A filtration problem through a heterogeneous porous medium

  • S. Challal

    King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
  • Abdeslem Lyaghfouri

    King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
A filtration problem through a heterogeneous porous medium cover

Abstract

The flow of a fluid through a heterogeneous porous medium is studied, assuming it is governed by a nonlinear Darcy law and Dirichlet boundary conditions. Under a general condition on the permeability we prove that the free boundary is locally a continuous curve in some local coordinates. We also prove the uniqueness of the Reservoirs-Connected Solution.