Vanishing viscosity limit for aggregation-diffusion equations - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Vanishing viscosity limit for aggregation-diffusion equations

Résumé

This article is devoted to the convergence analysis of the diffusive approximation of the measure-valued solutions to the so-called aggregation equation, which is now widely used to model collective motion of a population directed by an interaction potential. We prove, over the whole space in any dimension, a uniform-in-time convergence in Wasserstein distance, in the general framework of Lipschitz potentials, and provide a Op ? εq rate, where ε is the diffusion parameter, when the potential is λ´convex. We give an extension to some repulsive potentials and prove sharp convergence rates of the steady states towards the Dirac mass, under some uniform attractiveness assumptions.
Fichier principal
Vignette du fichier
Vanishing_viscosity_limit_for_aggregation_diffusion_equations-4.pdf (1.58 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04024118 , version 1 (10-03-2023)

Identifiants

  • HAL Id : hal-04024118 , version 1

Citer

Frédéric Lagoutière, Filippo Santambrogio, Sébastien Tran Tien. Vanishing viscosity limit for aggregation-diffusion equations. 2023. ⟨hal-04024118⟩
74 Consultations
57 Téléchargements

Partager

Gmail Facebook X LinkedIn More