| Issue |
ESAIM: ProcS
Volume 65, 2019
CEMRACS 2017 - Numerical methods for stochastic models: control, uncertainty quantification, mean-field
|
|
|---|---|---|
| Page(s) | 384 - 400 | |
| DOI | https://doi.org/10.1051/proc/201965384 | |
| Published online | 02 April 2019 | |
Numerical schemes for the aggregation equation with pointy potentials*
1
Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France
2
Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully, France
3
Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes, France
4
Laboratoire d’hydraulique Saint-Venant (École des Ponts ParisTech – EDF R&D – CEREMA), Université Paris-Est, 6 quai Watier, 78401 Chatou Cedex, France
5
Laboratoire J.-A. Dieudonné, UMR CNRS 7351, Univ. Nice, Parc Valrose, 06108 Nice Cedex 02, France
6
Université Paris 13, Sorbonne Paris Cité, CNRS UMR 7539, Laboratoire Analyse Géométrie et Applications, 93430 Villetaneuse, France
The aggregation equation is a nonlocal and nonlinear conservation law commonly used to describe the collective motion of individuals interacting together. When interacting potentials are pointy, it is now well established that solutions may blow up in finite time but global in time weak measure valued solutions exist. In this paper we focus on the convergence of particle schemes and finite volume schemes towards these weak measure valued solutions of the aggregation equation.
Résumé
L’équation dite d’agrégation est une loi de conservation nonlocale et nonlinéaire fréquemment utilisé pour décrire le comportement collectif d’individus en interacton. Quand le potentiel d’interaction est singulier, il est dorénavant bien connu que les solutions de l’équation d’agrégation explosent en temps fini. Cependant l’existence de solutions globales en temps à valeurs mesures a été établie. Dans ce travail, nous étudions la convergence de schémas particulaires et de schémas de volumes finis vers les solutions faibles de l’équation d’agrégation.
© EDP Sciences, SMAI 2019
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