The dam problem for nonlinear Darcy's laws and Dirichlet boundary conditions
- José Carrillo Menéndez 1
- Abdeslem Lyaghfouri 2
- 1 Universidad Complutense de Madrid, España
- 2 Universität Zürich, Switzerland
ISSN: 0391-173X
Year of publication: 1998
Volume: 26
Issue: 3
Pages: 453-505
Type: Article
More publications in: Annali della Scuola Normale Superiore di Pisa. Classe di scienze
Abstract
We study a free boundary problem related to a steady state fluid flow through a porous medium which is governed by a non linear Darcy’s law. A Dirichlet boundary condition is imposed on the top of the dam. Our main results are the continuity of the free boundary and the uniqueness of the S3-connected solution in the two dimensional case. For the general case, we prove the existence and uniqueness of a minimal solution.