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.
Cite this article
S. Challal, Abdeslem Lyaghfouri, A filtration problem through a heterogeneous porous medium. Interfaces Free Bound. 6 (2004), no. 1, pp. 55–79DOI 10.4171/IFB/91