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Hypocoercivity in Phi-entropy for the linear relaxation Boltzmann equation on the Torus

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorEvans, Josephine
dc.date.accessioned2019-10-12T13:02:03Z
dc.date.available2019-10-12T13:02:03Z
dc.date.issued2021
dc.identifier.issn0036-1410
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20113
dc.language.isoenen
dc.subjectConvergence to equilibrium
dc.subjectHypocoercivity
dc.subjectLinear Boltzmann Equation
dc.subjectφ-entropy
dc.subjectLogarithmic Sobolev inequality
dc.subjectBeckner Inequality
dc.subject.ddc515en
dc.titleHypocoercivity in Phi-entropy for the linear relaxation Boltzmann equation on the Torus
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper studies convergence to equilibrium for the spatially inhomogeneous linear relaxation Boltzmann equation in Boltzmann entropy and related entropy functionals, the p-entropies. Villani proved in [28] entropic hypocoercivity for a class of PDEs in a Hörmander sum of squares form. It was an open question to prove such a result for an operator which does not share this form. We prove a closed entropy-entropy production inequalityà la Villani which implies exponentially fast convergence to equilibrium for the linear Boltzmann equation with a quantitative rate. The key new idea appearing in our proof is the use of a total derivative of the entropy of a projection of our solution to compensate for an error term which appears when using non-linear entropies. We also extend the proofs for hypocoercivity for the linear relaxation Boltzmann to the case of Φ-entropy functionals.
dc.publisher.cityParisen
dc.relation.isversionofjnlnameSIAM Journal on Mathematical Analysis
dc.relation.isversionofjnlvol53
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2021
dc.relation.isversionofjnlpages18
dc.relation.isversionofdoi10.1137/19M1277631
dc.relation.isversionofjnlpublisherSIAM - Society for Industrial and Applied Mathematics
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2023-02-21T13:05:22Z
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