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| HAL : hal-00367518, version 3 |
| arXiv : 0903.2739 |
| DOI : 10.3233/ASY-2011-1031 |
| Fiche détaillée |  Récupérer au format |
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| Asymptotic Analysis 72, 3-4 (2011) 201-229 |
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| Versions disponibles : | v1 (16-03-2009) | v2 (20-01-2010) | v3 (07-12-2010) |
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| The grazing collision limit of Kac caricature of Bose-Einstein particles |
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| Thibaut Allemand 1Giuseppe Toscani 2 |
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| (2011) |
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| We discuss the grazing collision limit of certain kinetic models of Bose-Einstein particles obtained from a suitable modification of the one- dimensional Kac caricature of a Maxwellian gas without cut-off. We recover in the limit a nonlinear Fokker-Planck equation which presents many similarities with the one introduced by Kaniadakis and Quarati in [13 ]. In order to do so, we perform a study of the moments of the solution. Moreover, as is typical in Maxwell models, we make an essential use of the Fourier version of the equation. |
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| 1 : | Département de Mathématiques et Applications (DMA) |
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CNRS : UMR8553 – Ecole normale supérieure de Paris - ENS Paris |
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| 2 : | Dipartimento di matematica F. Casorati |
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Università degli studi di Pavia |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles Mathématiques/Physique mathématique Physique/Physique mathématique |
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| grazing collision – kinetic – Kac equation – Fokker-Planck equation |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00367518, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00367518 | |
| oai:hal.archives-ouvertes.fr:hal-00367518 | |
| Contributeur : Thibaut Allemand | |
| Soumis le : Mardi 7 Décembre 2010, 15:05:27 | |
| Dernière modification le : Mardi 3 Mai 2011, 09:33:49 | |
