Titre :

Convergence of a Degenerate Microscopic Dynamics to the Porous Medium Equation

Auteur(s) :

Blondel, Oriane [Auteur]
Probabilités, statistique, physique mathématique [PSPM]
Cancès, Clément [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Sasada, Makiko [Auteur]
Graduate School of Mathematical Sciences[Tokyo]
Simon, Marielle [Auteur]
Méthodes quantitatives pour les modèles aléatoires de la physique [MEPHYSTO-POST]

Éditeur :

Association des Annales de l'Institut Fourier

Date de publication :

2019

Discipline(s) HAL :

Mathématiques [math]/Probabilités [math.PR]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Physique [physics]/Matière Condensée [cond-mat]/Mécanique statistique [cond-mat.stat-mech]

Résumé en anglais : [en]

We derive the porous medium equation from an interacting particle system which belongs to the family of exclusion processes, with nearest neighbor exchanges. The particles follow a degenerate dynamics, in the sense that ...
Lire la suite >We derive the porous medium equation from an interacting particle system which belongs to the family of exclusion processes, with nearest neighbor exchanges. The particles follow a degenerate dynamics, in the sense that the jump rates can vanish for certain configurations, and there exist blocked configurations that cannot evolve. In [7] it was proved that the macroscopic density profile in the hydrodynamic limit is governed by the porous medium equation (PME), for initial densities uniformly bounded away from 0 and 1. In this paper we consider the more general case where the density can take those extreme values. In this context, the PME solutions display a richer behavior, like moving interfaces, finite speed of propagation and breaking of regularity. As a consequence, the standard techniques that are commonly used to prove this hydrodynamic limits cannot be straightforwardly applied to our case. We present here a way to generalize the relative entropy method, by involving approximations of solutions to the hydrodynamic equation, instead of exact solutions.Lire moins >

Langue :

Anglais

Projet ANR :

Modèles stochastiques en grande dimension pour la physique statistique hors équilibre
Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Approche géométrique pour les écoulements en milieux poreux: théorie et numérique
Community of mathematics and fundamental computer science in Lyon
Marches aléatoires en interaction
Diffusion de l'énergie dans des systèmes hamiltoniens bruitésés

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL