Titre :

Long time behavior of the field-road diffusion model: an entropy method and a finite volume scheme

Auteur(s) :

Alfaro, Matthieu [Auteur]
Laboratoire de Mathématiques Raphaël Salem [LMRS]
Chainais-Hillairet, Claire [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]

Mot(s)-clé(s) en anglais :

field-road model long time behavior finite-volume method entropy dissipation entropy construction method functional inequalities AMS Subject Classifications: 35K40 35B40 65M08 65M12
field-road model
long time behavior
finite-volume method
entropy dissipation
entropy construction method
functional inequalities

Discipline(s) HAL :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]

Résumé en anglais : [en]

We consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions (a {\it field} and a {\it road} in a population dynamics context) and ...
Lire la suite >We consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions (a {\it field} and a {\it road} in a population dynamics context) and coupled through exchange terms on the road, which makes its analysis quite involved. We propose a TPFA finite volume scheme. In both the continuous and the discrete settings, we prove theexponential decay of an entropy, and thus the long time convergence to the stationary state selected by the total mass of the initial data. To deal with the problem of different dimensions, we artificially \lq\lq thicken'' the road and, then, establish a rather unconventional Poincaré-Wirtinger inequality. Numerical simulations confirm and complete the analysis, and raise new issues.Lire moins >

Langue :

Anglais

Projet ANR :

Modèles intégro-différentiels venant de la biologie évolutive
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL