Generalized solutions of a kinetic granular media equation by a gradient flow approach

Agueh, Martial; Carlier, Guillaume

Agueh, Martial; Carlier, Guillaume (2015), Generalized solutions of a kinetic granular media equation by a gradient flow approach, Calculus of Variations and Partial Differential Equations, 55, 2. 10.1007/s00526-016-0978-7

Type

Article accepté pour publication ou publié

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https://hal.archives-ouvertes.fr/hal-01164843

Date

2015-06

Nom de la revue

Calculus of Variations and Partial Differential Equations

Volume

Numéro

Éditeur

Springer

Identifiant publication

10.1007/s00526-016-0978-7

Métadonnées

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Auteur(s)

Agueh, Martial
Pacific Institut for Mathematical Sciences [PIMS]
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

Résumé (EN)

We consider a one-dimensional kinetic model of granular media in the case where the interaction potential is quadratic. Taking advantage of a simple first integral, we can use a reformulation (equivalent to the initial kinetic model for classical solutions) which allows measure solutions. This reformulation has a Wasserstein gradient flow structure (on a possibly infinite product of spaces of measures) for a convex energy which enables us to prove global in time well-posedness.

Mots-clés

Kinetic models of granular media; product Wasserstein space; Gradient flows