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dc.contributor.authorMischler, Stéphane*
dc.contributor.authorMouhot, Clément*
dc.date.accessioned2017-12-01T09:46:42Z
dc.date.available2017-12-01T09:46:42Z
dc.date.issued2016
dc.identifier.issn0003-9527
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17133
dc.language.isoenen
dc.subjectFokker-Planck equation
dc.subjectKolmogorov-Fokker-Planck equation
dc.subjecthypocoercivity
dc.subjecthypodissipativity
dc.subjectspectral mapping theorem
dc.subjectsemigroup
dc.subjectenlargement
dc.subjectspectral gap
dc.subject.ddc515en
dc.titleExponential stability of slowly decaying solutions to the kinetic Fokker-Planck equation
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThe aim of the present paper is twofold:(1) We carry on with developing an abstract method for deriving decay estimates on the semigroup associated to non-symmetric operators in Banach spaces as introduced in [10]. We extend the method so as to consider the shrinkage of the functional space. Roughly speaking, we consider a class of operators writing as a dissipative part plus a mild perturbation, and we prove that if the associated semigroup satisfies a decay estimate in some reference space then it satisfies the same decay estimate in another—smaller or larger—Banach space under the condition that a certain iterate of the “mild perturba- tion” part of the operator combined with the dissipative part of the semigroup maps the larger space to the smaller space in a bounded way. The cornerstone of our approach is a factorization argument, reminiscent of the Dyson series.(2) We apply this method to the kinetic Fokker-Planck equation when the spatial domain is either the torus with periodic boundary conditions, or the whole space with a confinement potential. We then obtain spectral gap es- timates for the associated semigroup for various metrics, including Lebesgue norms, negative Sobolev norms, and the Monge-Kantorovich-Wasserstein distance W_1.
dc.relation.isversionofjnlnameArchive for Rational Mechanics and Analysis
dc.relation.isversionofjnlvol221
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2016
dc.relation.isversionofjnlpages677-723
dc.relation.isversionofdoi10.1007/s00205-016-0972-4
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
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dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-12-19T09:47:03Z
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hal.person.labIds60*


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