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Zeitschrift für Analysis und ihre Anwendungen


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Volume 23, Issue 2, 2004, pp. 335–351
DOI: 10.4171/ZAA/1202

Published online: 2004-06-30

Asymptotic Behavior of the Solutions of an Elliptic-Parabolic System Arising in Flow in Porous Media

Y. Amirat[1] and A. Ziani[2]

(1) Université Blaise Pascal, Aubière, France
(2) Université de Nantes, France

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

Amirat Y., Ziani A.: Asymptotic Behavior of the Solutions of an Elliptic-Parabolic System Arising in Flow in Porous Media. Z. Anal. Anwend. 23 (2004), 335-351. doi: 10.4171/ZAA/1202