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

Ait Hammou Oulhaj, Ahmed; Cancès, Clément; Chainais-Hillairet, Claire; Laurençot, Philippe

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.4171/IFB/421

Title :

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

Author(s) :

Ait Hammou Oulhaj, Ahmed [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]
Cancès, Clément [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Chainais-Hillairet, Claire [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]
Laurençot, Philippe [Auteur]
Institut de Mathématiques de Toulouse UMR5219 [IMT]

Journal title :

Interfaces and Free Boundaries : Mathematical Analysis, Computation and Applications

Pages :

199-229

Publisher :

European Mathematical Society

Publication date :

2019

ISSN :

1463-9963

English keyword(s) :

Muskat problem
Cross-diffusion system
Two-phase porous media flows
large time behavior

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Approche géométrique pour les écoulements en milieux poreux: théorie et numérique
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :