The Dam Problem for Nonlinear Darcy's Laws and Dirichlet Boundary Conditions

José Carrillo, Abdeslem Lyaghfouri

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)453-505
Number of pages53
JournalAnnali della Scuola normale superiore di Pisa - Classe di scienze
Volume26
Issue number3
Publication statusPublished - 1998
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Mathematics (miscellaneous)

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