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Nonuniqueness of Steady State Fingering Solutions in Porous Media
Author(s) -
Var James E.,
Greenkorn Robert A.
Publication year - 1970
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr006i005p01411
Subject(s) - steady state (chemistry) , porous medium , viscous fingering , boundary value problem , position (finance) , mathematics , mathematical analysis , mechanics , porosity , physics , geology , geotechnical engineering , chemistry , economics , finance
Steady state solutions for single viscous fingers are nonunique because the position of the interfacial boundary is not specified. Expanding the steady state problem to include an arbitrary number of fingers does not make the solution unique. The initial value problem however does have a unique solution, which suggests that it is futile to look for additional conservation type equations in the hope of making the steady state solutions unique.