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

José Carrillo; Abdeslem Lyaghfouri

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

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	453-505
Number of pages	53
Journal	Annali della Scuola normale superiore di Pisa - Classe di scienze
Volume	26
Issue number	3
Publication status	Published - 1998
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Mathematics (miscellaneous)

Cite this

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AB - 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.

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

Abstract

ASJC Scopus subject areas

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