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Diffusion limit for a kinetic equation with a thermostatted interface

hal.structure.identifierDipartimento di Matematica "Guido Castelnuovo" [Roma I] [Sapienza University of Rome]
dc.contributor.authorBasile, Giada*
hal.structure.identifierInstitut of Mathematics - Polish Academy of Sciences [PAN]
dc.contributor.authorKomorowski, Tomasz*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorOlla, Stefano
HAL ID: 18345
ORCID: 0000-0003-0845-1861		*
dc.date.accessioned2019-03-26T08:56:09Z
dc.date.available2019-03-26T08:56:09Z
dc.date.issued2019
dc.identifier.issn1937-5093
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18572
dc.language.isoenen
dc.subjectDiffusion limit
dc.subjectthermostatted boundary conditions
dc.subject.ddc519en
dc.titleDiffusion limit for a kinetic equation with a thermostatted interface
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider a linear phonon Boltzmann equation with a reflecting/transmitting/absorbing interface. This equation appears as the Boltzmann-Grad limit for the energy density function of a harmonic chain of oscillators with inter-particle stochastic scattering in the presence of a heat bath at temperature T in contact with one oscillator at the origin. We prove that under the diffusive scaling the solutions of the phonon equation tend to the solution ρ(t, y) of a heat equation with the boundary condition ρ(t, 0) ≡ T .
dc.publisher.cityParisen
dc.relation.isversionofjnlnameKinetic & Related Models
dc.relation.isversionofjnlvol12
dc.relation.isversionofjnlissue5
dc.relation.isversionofjnldate2019
dc.relation.isversionofjnlpages1185-1196
dc.relation.isversionofdoi10.3934/krm.2019045
dc.relation.isversionofjnlpublisherAIMS - American Institute of Mathematical Sciences
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenon
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dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2020-04-22T14:21:41Z
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