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

• José Carrillo ^[1] ; Abdeslem Lyaghfouri ^[2]
  1. [1] Universidad Complutense de Madrid

     Universidad Complutense de Madrid

     Madrid, España

     
  2. [2] University of Zurich

     University of Zurich

     Zürich, Suiza

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 26, Nº 3, 1998, págs. 453-505
• Idioma: inglés
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• 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.