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| HAL : hal-00521216, version 2 |
| arXiv : 1009.5166 |
| Fiche détaillée |  Récupérer au format |
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| Mathematical Models and Methods in Applied Sciences 21, 11 (2011) 2179-2210 |
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| Versions disponibles : | v1 (27-09-2010) | v2 (03-12-2010) |
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| Stochastic Mean-Field Limit: Non-Lipschitz Forces & Swarming |
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François Bolley 1José Cañizo 2 |
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| (2011) |
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| We consider general stochastic systems of interacting particles with noise which are relevant as models for the collective behavior of animals, and rigorously prove that in the mean-field limit the system is close to the solution of a kinetic PDE. Our aim is to include models widely studied in the literature such as the Cucker-Smale model, adding noise to the behavior of individuals. The difficulty, as compared to the classical case of globally Lipschitz potentials, is that in several models the interaction potential between particles is only locally Lipschitz, the local Lipschitz constant growing to infinity with the size of the region considered. With this in mind, we present an extension of the classical theory for globally Lipschitz interactions, which works for only locally Lipschitz ones. |
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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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| Mean-field limit – diffusion – Cucker-Smale – collective behavior |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00521216, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00521216 | |
| oai:hal.archives-ouvertes.fr:hal-00521216 | |
| Contributeur : François Bolley | |
| Soumis le : Mercredi 1 Décembre 2010, 13:49:30 | |
| Dernière modification le : Mercredi 11 Janvier 2012, 15:50:51 | |
