Large time behavior of a two phase extension of the porous medium equation

  • Ahmed Ait Hammou Oulhaj

    Université de Technologie de Compiègne, France
  • Clément Cancès

    Université de Lille, France
  • Claire Chainais-Hillairet

    Université de Lille, France
  • Philippe Laurençot

    Université de Toulouse, France
Large time behavior of a two phase extension of the porous medium equation cover
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Abstract

We study the large time behavior of the solutions to a two phase extension of the porous medium equation, which models the so-called seawater intrusion problem. The goal is to identify the self-similar solutions that correspond to steady states of a rescaled version of the problem. We fully characterize the unique steady states that are identified as minimizers of a convex energy and shown to be radially symmetric. Moreover, we prove the convergence of the solution to the time-dependent model towards the unique stationary state as time goes to infinity. We finally provide numerical illustrations of the stationary states and we exhibit numerical convergence rates.

Cite this article

Ahmed Ait Hammou Oulhaj, Clément Cancès, Claire Chainais-Hillairet, Philippe Laurençot, Large time behavior of a two phase extension of the porous medium equation. Interfaces Free Bound. 21 (2019), no. 2, pp. 199–229

DOI 10.4171/IFB/421