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| HAL : hal-00586008, version 2 |
| arXiv : 1104.2985 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (15-04-2011) | v2 (20-04-2011) |
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| A Class of Non-Local Models for Pedestrian Traffic |
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| Rinaldo M. Colombo 1Mauro Garavello 2 |
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| (14/04/2011) |
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| We present a new class of macroscopic models for pedestrian flows. Each individual is assumed to move towards a fixed target, deviating from the best path according to the instantaneous crowd distribution. The resulting equation is a conservation law with a nonlocal 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. Specific models are presented and their qualitative properties are shown through numerical integrations. |
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| 1 : | Dipartimento di Matematica [Universita di Brescia] |
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Università di Brescia |
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| 2 : | Dipartimento di Scienze e Tecnologie Avanzate (DISTA) |
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Università del Piemonte Orientale |
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| 3 : | Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO) |
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Université d'Orléans – CNRS : UMR7349 |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Crowd Dynamics – Macroscopic Pedestrian Model – Non-Local Conservation Laws. |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00586008, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00586008 | |
| oai:hal.archives-ouvertes.fr:hal-00586008 | |
| Contributeur : Magali Lécureux-Mercier | |
| Soumis le : Vendredi 15 Avril 2011, 11:16:01 | |
| Dernière modification le : Mercredi 20 Avril 2011, 08:14:36 | |
