Show simple item record

dc.contributor.authorTristani, Isabelle
dc.date.accessioned2013-12-03T13:51:00Z
dc.date.available2013-12-03T13:51:00Z
dc.date.issued2016
dc.identifier.issn0022-1236
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/12235
dc.language.isoenen
dc.subjectelastic limit
dc.subjectlong-time asymptotic
dc.subjectperturbation
dc.subjectInelastic Boltzmann equation
dc.subjectexponential rate of convergence
dc.subjectviscoelastic hard-spheres
dc.subjectsmall diffusion parameter
dc.subjectgranular media
dc.subjectspectral gap
dc.subject.ddc515en
dc.titleBoltzmann equation for granular media with thermal force in a weakly inhomogeneous setting
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper, we consider the spatially inhomogeneous diffusively driven inelastic Boltzmann equation in different cases: the restitution coefficient can be constant or can depend on the impact velocity (which is a more physically relevant case), including in particular the case of viscoelastic hard-spheres. In the weak thermalization regime, i.e when the diffusion parameter is sufficiently small, we prove existence of global solutions considering both the close-to-equilibrium and the weakly inhomogeneous regimes. We also study the long-time behavior of these solutions and prove a convergence to equilibrium with an exponential rate. The basis of the proof is the study of the linearized equation. We obtain a new result on it, we prove existence of a spectral gap in weighted (stretched exponential and polynomial) Sobolev spaces, more precisely, there is a one-dimensional eigenvalue which is negative and which tends to $0$ when the diffusion parameter tends to $0$. To do that, we take advantage of the recent paper \cite{GMM} where the spatially inhomogeneous equation for elastic hard spheres has been considered. As far as the case of a constant coefficient is concerned, the present paper improves similar results obtained in \cite{MM2} in a spatially homogeneous framework. Concerning the case of a non-constant coefficient, this kind of results is new and we use results on steady states of the linearized equation from \cite{AL3}.
dc.publisher.cityParisen
dc.relation.isversionofjnlnameJournal of Functional Analysis
dc.relation.isversionofjnlvol270
dc.relation.isversionofjnlissue5
dc.relation.isversionofjnldate2016
dc.relation.isversionofjnlpages1922-1970
dc.relation.isversionofdoi10.1016/j.jfa.2015.09.025
dc.relation.isversionofjnlpublisherAcademic Press
dc.subject.ddclabelAnalyseen
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2016-10-12T15:14:32Z


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record