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.
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Y. Amirat, A. Ziani, Asymptotic Behavior of the Solutions of an Elliptic-Parabolic System Arising in Flow in Porous Media. Z. Anal. Anwend. 23 (2004), no. 2, pp. 335–351DOI 10.4171/ZAA/1202