Karam Allali, Vitaly Volpert, Vitali Vougalter
Abstract:
In this article we study the interaction of two miscible liquids in
porous media. The model consists of hydrodynamic equations with the
Korteweg stress terms coupled with the reaction-diffusion equation for
the concentration. We assume that the fluid is incompressible and its
motion is described by the Darcy law. The global existence and
uniqueness of solutions is established for some optimal conditions
on the reaction source term and external force functions.
Numerical simulations are performed to show the behavior of two
miscible liquids subjected to the Korteweg stress.
Submitted June 3, 2015. Published October 12, 2015.
Math Subject Classifications: 35A01, 35A02, 76D03, 76S05.
Key Words: Darcy approximation; Korteweg stress; miscible liquids;
porous media.
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Karam Allali Department of Mathematics Faculty of Sciences and Technologies University Hassan II PO Box 146, Mohammedia, Morocco email: allali@fstm.ac.ma |
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Vitaly Volpert Institute Camille Jordan University Lyon 1, UMR 5208 CNRS 69622 Villeurbanne, France email: volpert@math.univ-lyon1.fr |
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Vitali Vougalter University of Toronto Department of Mathematics Toronto, ON, M5S 2E4, Canada email: vitali@math.toronto.edu |
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