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| HAL : hal-00482286, version 1 |
| arXiv : 1005.1495 |
| Fiche détaillée |  Récupérer au format |
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| Hypocoercivity for linear kinetic equations conserving mass |
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Jean Dolbeault 1Clément Mouhot 2, 3 |
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| (10/05/2010) |
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| We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models like the linear Boltzmann equation or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. |
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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 : | Département de Mathématiques et Applications (DMA) |
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CNRS : UMR8553 – Ecole Normale Supérieure de Paris - ENS Paris |
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| 3 : | DAMTP/CMS Univ. Cambridge (DAMTP) |
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University of Cambridge |
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| 4 : | Fakultät für Mathematik |
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Universität Wien |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles Mathématiques/Théorie spectrale |
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| kinetic equations – hypocoercivity – Boltzmann – BGK – relaxation – diffusion limit – nonlinear diffusion – Fokker-Planck – confinement – spectral gap – Poincaré inequality – Hardy-Poincaré inequality |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00482286, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00482286 | |
| oai:hal.archives-ouvertes.fr:hal-00482286 | |
| Contributeur : Clément Mouhot | |
| Soumis le : Lundi 10 Mai 2010, 10:49:19 | |
| Dernière modification le : Lundi 10 Mai 2010, 13:19:04 | |
