DAMBRINE, Julien; MEUNIER, Nicolas; MAURY, Bertrand; ROUDNEFF-CHUPIN, Aude

doi:10.3934/cpaa.2012.11.243

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

DAMBRINE, Julien
Institut de Mathématiques de Bordeaux [IMB]

MEUNIER, Nicolas
Mathématiques Appliquées Paris 5 [MAP5 - UMR 8145]

MAURY, Bertrand
Laboratoire de Mathématiques d'Orsay [LMO]

Langue

Article de revue

Ce document a été publié dans

Communications on Pure and Applied Mathematics. 2012, vol. 11, n° 1, p. 243-260

Wiley

Résumé en anglais

This paper deals with a class of macroscopic models for cell migration in a saturated medium for two-species mixtures. Those species tend to achieve some motion according to a desired velocity, and congestion forces them to adapt their velocity. This adaptation is modelled by a correction velocity which is chosen minimal in a least-square sense. We are especially interested in two situations: a single active species moves in a passive matrix (cell migration) with a given desired velocity, and a closed-loop Keller-Segel type model, where the desired velocity is the gradient of a self-emitted chemoattractant. We propose a theoretical framework for the open-loop model (desired velocities are defined as gradients of given functions) based on a formulation in the form of a gradient flow in the Wasserstein space. We propose a numerical strategy to discretize the model, and illustrate its behaviour in the case of a prescribed velocity, and for the saturated Keller-Segel model.< Réduire