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| HAL : hal-00563915, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Applied Mathematics Letters 25, 3 (2012) 339-343 |
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| Mean-field limit for the stochastic Vicsek model |
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| François Bolley 1José Cañizo 2 |
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| (2012) |
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| We consider the continuous version of the Vicsek model with noise, proposed as a model for collective behavior of individuals with a fixed speed. We rigorously derive the kinetic mean-field partial differential equation satisfied when the number $N$ of particles tends to infinity, quantifying the convergence of the law of one particle to the solution of the PDE. For this we adapt a classical coupling argument to the present case in which both the particle system and the PDE are defined on a surface rather than on the whole space $\rr^d$. As part of the study we give existence and uniqueness results for both the particle system and the PDE. |
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| 1 : | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| 2 : | Departament de Matemàtiques [Barcelona] |
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Universitat Autónoma Barcelona |
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| Domaine | : | Mathématiques/Probabilités Mathématiques/Equations aux dérivées partielles |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00563915, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00563915 | |
| oai:hal.archives-ouvertes.fr:hal-00563915 | |
| Contributeur : François Bolley | |
| Soumis le : Lundi 7 Février 2011, 15:43:15 | |
| Dernière modification le : Mercredi 11 Janvier 2012, 15:50:06 | |
