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Numerical schemes for the aggregation equation with pointy potentials

Benoît Fabrèges 1 Hélène Hivert 2 Kévin Le Balc’h 3 Sofiane Martel 4 François Delarue 5 Frédéric Lagoutière 2 Nicolas Vauchelet 6 
1 ICJ - Institut Camille Jordan [Villeurbanne]
2 MMCS - Modélisation mathématique, calcul scientifique
ICJ - Institut Camille Jordan [Villeurbanne]
3 IRMAR - Institut de Recherche Mathématique de Rennes
4 Saint-Venant - Laboratoire d'Hydraulique Saint-Venant / Saint-Venant laboratory for Hydraulics
5 JAD - Laboratoire Jean Alexandre Dieudonné
6 LAGA - Laboratoire Analyse, Géométrie et Applications
Abstract : 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.
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UNIV-ST-ETIENNE | UNIV-PARIS13 | ENPC | UNIV-RENNES1 | UNIV-PARIS8 | IRMAR | UR2-HB | CNRS | ICJ | UNIV-LYON1 | INSA-LYON | INSA-RENNES | EC-LYON | LAGA | INSMI | PARISTECH | DIEUDONNE | ENPC-LHSV | UNAM | IRMAR-AN | ENS-RENNES | CHL | TDS-MACS | USPC | UR1-MATH-STIC | CEREMA | UNIV-RENNES2 | EDF | GALILE | ICJ-MMCS | UNIV-COTEDAZUR | UNIV-RENNES | INSA-GROUPE | UNIV-PARIS-LUMIERES | UDL | SORBONNE-PARIS-NORD | UR1-MATH-NUM | UNIV-PARIS8-OA

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Benoît Fabrèges, Hélène Hivert, Kévin Le Balc’h, Sofiane Martel, François Delarue, et al.. Numerical schemes for the aggregation equation with pointy potentials. ESAIM: Proceedings and Surveys, EDP Sciences, 2019, ⟨10.1051/proc/201965384⟩. ⟨hal-01788050⟩

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