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Issue ESAIM: PROC
Volume 18, 2007
Paris-sud working group on modelling and scientific computing 2006-2007
Page(s) 143 - 152
DOI 10.1051/proc:071812
Published online 12 September 2007

ESAIM: Proc., 2007, Vol. 18, pp. 143-152
DOI: 10.1051/proc:071812

Un Modèle de Mouvements de Foule

Bertrand MAURY and Juliette VENEL

Laboratoire de Mathématiques, Université Paris XI, Orsay,

prenom.nom@math.u-psud.fr

(Published online: 12 September 2007)

Abstract
We propose a deterministic model for crowd motion, based on a Lagrangian approach: each person is taken into account individually. We are especially interested in the modelling of evacuation: people are willing to exit a room with obstacles. The model takes the form of an evolution equation which involves a multivalued operator, which is not in general maximal monotone. Using recent results on the sweeping process, we establish the well-posedness of this problem under reasonable assumptions. We propose a numerical scheme, which we apply to two realistic situations.


Résumé
Nous proposons un modèle déterministe de mouvements de foule basé sur une approche Lagrangienne où chaque individu est pris en compte. Nous nous intéressons ici à la modélisation de situations d'évacuation : des personnes veulent quitter une salle pouvant contenir des obstacles (tables, piliers). Nous aboutissons à une équation d'évolution sur la position où intervient un opérateur multivalué. La difficulté provient du fait que cet opérateur n'est pas en général maximal monotone. À partir de résultats récents sur le processus de rafle, nous établissons le caractère bien posé du problème. Nous présentons un schéma numérique que nous appliquons à la simulation de deux situations réalistes.


Mathematics Subject Classification. 47H04, 34A60, 90C46

Key words: crowd motion, differential inclusion, sweeping process, prox-regular set, catch-up algorithm


© EDP Sciences, ESAIM 2007


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