Asymptotic Behavior of the Solutions of an Elliptic-Parabolic System Arising in Flow in Porous Media
Y. Amirat
Université Blaise Pascal, Aubière, FranceA. Ziani
Université de Nantes, France
![Asymptotic Behavior of the Solutions of an Elliptic-Parabolic System Arising in Flow in Porous Media cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-zaa-volume-23-issue-2.png&w=3840&q=90)
Abstract
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.
Cite this article
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. 335–351
DOI 10.4171/ZAA/1202