[Dynamique non locale des foules]
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.
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@article{CRMATH_2011__349_13-14_769_0,
author = {Colombo, Rinaldo M. and Garavello, Mauro and L\'ecureux-Mercier, Magali},
title = {Non-local crowd dynamics},
journal = {Comptes Rendus. Math\'ematique},
pages = {769--772},
publisher = {Elsevier},
volume = {349},
number = {13-14},
year = {2011},
doi = {10.1016/j.crma.2011.07.005},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.crma.2011.07.005/}
}
TY - JOUR AU - Colombo, Rinaldo M. AU - Garavello, Mauro AU - Lécureux-Mercier, Magali TI - Non-local crowd dynamics JO - Comptes Rendus. Mathématique PY - 2011 SP - 769 EP - 772 VL - 349 IS - 13-14 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2011.07.005/ DO - 10.1016/j.crma.2011.07.005 LA - en ID - CRMATH_2011__349_13-14_769_0 ER -
%0 Journal Article %A Colombo, Rinaldo M. %A Garavello, Mauro %A Lécureux-Mercier, Magali %T Non-local crowd dynamics %J Comptes Rendus. Mathématique %D 2011 %P 769-772 %V 349 %N 13-14 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.crma.2011.07.005/ %R 10.1016/j.crma.2011.07.005 %G en %F CRMATH_2011__349_13-14_769_0
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. https://www.numdam.org/articles/10.1016/j.crma.2011.07.005/
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