The heterogeneous dam problem with leaky boundary condition

S. Challal, A. Lyaghfouri

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We study the heterogeneous dam problem, assuming the ux at the bottoms of the reservoirs obeying to a nonlinear law called leaky boundary condition. The velocity and the pressure are related by a nonlinear Darcy's law. Under a general monotonicity hypothesis on the permeability matrix, we prove that the free boundary is represented locally by graphs of continuous functions. We also prove the uniqueness of minimal and maximal solutions. When the ow is given by a linear Darcy law and the permeability matrix is symmetric, we prove the uniqueness of the reservoirs-connected solution.

Original languageEnglish
Pages (from-to)93-125
Number of pages33
JournalCommunications on Pure and Applied Analysis
Volume10
Issue number1
DOIs
Publication statusPublished - Jan 2011
Externally publishedYes

Keywords

  • Dam Problem
  • Darcy law
  • Free boundary
  • Leaky boundary condition

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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