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A One‐dimensional flow problem in porous media with hydrophile grains
Author(s) -
Fasano A.
Publication year - 1999
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(19990510)22:7<605::aid-mma55>3.0.co;2-x
Subject(s) - porous medium , mathematics , porosity , wetting , stefan problem , free boundary problem , saturation (graph theory) , richards equation , flow (mathematics) , absorption (acoustics) , boundary value problem , mechanics , boundary (topology) , mathematical analysis , calculus (dental) , thermodynamics , materials science , geometry , physics , composite material , geotechnical engineering , geology , combinatorics , water content , medicine , dentistry
We study a free boundary problem describing the propagation of the wetting front following the injection of a liquid into a porous medium with hydrophile granules. The absorption process produces a non‐local interaction with the flow so that the porosity appearing in the parabolic equation for pressure is a functional of saturation and of the free boundary. Our analysis is confined to the unsaturated regime, which is the first stage of the process. An existence theorem is proved. Copyright © 1999 John Wiley & Sons, Ltd.