Asymptotic Behavior of the Solutions of an Elliptic-Parabolic System Arising in Flow in Porous Media
Youcef Amirat, Abdelhamid Ziani · Zeitschrift für Analysis und ihre Anwendungen · 2004
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.