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The dam problem for non‐linear Darcy's laws and non‐linear leaky boundary conditions
Author(s) -
Chipot M.,
Lyaghfouri A.
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199708)20:12<1045::aid-mma900>3.0.co;2-3
Subject(s) - darcy's law , mathematics , boundary value problem , boundary (topology) , law , simple (philosophy) , flow (mathematics) , mathematical analysis , calculus (dental) , porous medium , porosity , geometry , geology , geotechnical engineering , political science , medicine , philosophy , dentistry , epistemology
The goal of this paper is to establish that even for strongly non‐linear Darcy's laws and strongly non‐linear leaky boundary conditions on the bottom of the reservoirs the fluid flow through a porous dam is a well‐posed problem for which existence of a solution can be established. In a simple case we provide also the exact solution to the problem. © 1997 B. G. Teubner Stuttgart–John Wiley & Sons Ltd.