The dam problem for nonlinear Darcy's laws and Dirichlet boundary conditions

  1. José Carrillo Menéndez 1
  2. Abdeslem Lyaghfouri 2
  1. 1 Universidad Complutense de Madrid, España
  2. 2 Universität Zürich, Switzerland
Revista:
Annali della Scuola Normale Superiore di Pisa. Classe di scienze

ISSN: 0391-173X

Año de publicación: 1998

Volumen: 26

Número: 3

Páginas: 453-505

Tipo: Artículo

Otras publicaciones en: Annali della Scuola Normale Superiore di Pisa. Classe di scienze

Resumen

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.