JournalszaaVol. 23 , No. 2DOI 10.4171/zaa/1202

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

  • Y. Amirat

    Université Blaise Pascal, Aubière, France
  • A. Ziani

    Université de Nantes, France
Asymptotic Behavior of the Solutions of an Elliptic-Parabolic System Arising in Flow in Porous Media cover

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.