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dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
dc.contributor.authorMouhot, Clément
HAL ID: 1892
dc.contributor.authorSchmeiser, Christian
dc.date.accessioned2010-06-03T12:49:50Z
dc.date.available2010-06-03T12:49:50Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/4271
dc.language.isoenen
dc.subjecthypocoercivityen
dc.subjectPoincaré inequalityen
dc.subjectkinetic equationsen
dc.subjectHardy-Poincaré inequalityen
dc.subjectspectral gapen
dc.subjectconfinementen
dc.subjectFokker-Plancken
dc.subjectnonlinear diffusionen
dc.subjectdiffusion limiten
dc.subjectrelaxationen
dc.subjectBGKen
dc.subjectBoltzmannen
dc.subject.ddc515en
dc.titleHypocoercivity for linear kinetic equations conserving massen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe 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.en
dc.identifier.citationpages21en
dc.relation.isversionofjnlnameTransactions of the American Mathematical Society
dc.relation.isversionofjnldate2012
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00482286/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherAmerican Mathematical Society
dc.subject.ddclabelAnalyseen


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