Zeitschrift für Analysis und ihre Anwendungen 23 (2004), No. 2, 335--351
Copyright Heldermann Verlag 2004
Asymptotic Behavior of the Solutions of an Elliptic-Parabolic System Arising in Flow in Porous Media
Y. Amirat
Université B. Pascal, Lab. de Mathématique Applique, CNRS UMR 6620, 63177 Aubière, France
amirat@math.univ-bpclermont.fr
A. Ziani
Université de Nantes, Dép. de Mathématique, B.P. 92208, 44322 Nantes Cedex 3, France
ziani@math.univ-nantes.fr
We study the asymptotic behavior, with respect to high Peclet numbers, of the solutions of the nonlinear elliptic-parabolic system governing the displacement of one incompressible fluid by another, completely miscible with the first, in a porous medium. Using compensated compactness techniques, we obtain the existence of a global weak solution to the nonlinear degenerate elliptic-parabolic system modelling the flow when the molecular diffusion effects are neglected.
Keywords: Nonlinear degenerate elliptic-parabolic systems, miscible flow in porous media.
MSC: 35D05; 35K60, 35K65, 76S05
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