no. 13-14
Partial Differential Equations
Non-local crowd dynamics
[Dynamique non locale des foules]

Présenté par : the Editorial Board

Colombo, Rinaldo M.1 ; Garavello, Mauro2 ; Lécureux-Mercier, Magali3
1 Dipartimento di Matematica, Università degli studi di Brescia, Via Branze 38, 25123 Brescia, Italy
2 Di.S.T.A., Università del Piemonte Orientale, Viale Teresa Michel 11, 15121 Alessandria, Italy
3 Université dʼOrléans, bâtiment de mathématiques, rue de Chartres, B.P. 6759, 45067 Orléans cedex 2, France
Comptes Rendus. Mathématique, Tome 349 (2011) no. 13-14, pp. 769-772.

Nous présentons ici un nouveau modèle macroscopique de trafic piéton dans lequel chaque individu se dirige vers une cible fixe en déviant du plus court chemin en fonction de la distribution de la population. On obtient une loi de conservation avec flux non local qui génère un semi-groupe de solutions et est stable par rapport aux fonctions et paramètres quʼelle contient. On montre de plus que la densité reste bornée pour tout temps. On sʼintéresse plus particuliérement à deux modèles précis.

We present a new class of macroscopic models for pedestrian flows. Each individual is assumed to move toward a fixed target, deviating from the best path according to the crowd distribution. The resulting equation is a conservation law with a non-local flux. Each equation in this class generates a Lipschitz semigroup of solutions and is stable with respect to the functions and parameters defining it. Moreover, key qualitative properties such as the boundedness of the crowd density are proved. Two specific models in this class are considered.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.07.005
Colombo, Rinaldo M. 1 ; Garavello, Mauro 2 ; Lécureux-Mercier, Magali 3

1 Dipartimento di Matematica, Università degli studi di Brescia, Via Branze 38, 25123 Brescia, Italy
2 Di.S.T.A., Università del Piemonte Orientale, Viale Teresa Michel 11, 15121 Alessandria, Italy
3 Université dʼOrléans, bâtiment de mathématiques, rue de Chartres, B.P. 6759, 45067 Orléans cedex 2, France 
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Colombo, Rinaldo M.; Garavello, Mauro; Lécureux-Mercier, Magali. Non-local crowd dynamics. Comptes Rendus. Mathématique, Tome 349 (2011) no. 13-14, pp. 769-772. doi : 10.1016/j.crma.2011.07.005. http://www.numdam.org/articles/10.1016/j.crma.2011.07.005/

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