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Relaxation rate, diffusion approximation and Fick's law for inelastic scattering Boltzmann models

dc.contributor.authorLods, Bertrand
dc.contributor.authorMouhot, Clément
HAL ID: 1892
dc.contributor.authorToscani, Giuseppe
dc.date.accessioned2009-07-06T15:00:30Z
dc.date.available2009-07-06T15:00:30Z
dc.date.issued2008
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/839
dc.language.isoenen
dc.subjectlinear Boltzmann equation
dc.subjectentropy production
dc.subjectspectral gap
dc.subjectdiffusion approximation
dc.subjectFick's law
dc.subjectdiffusive coefficient
dc.subjectGranular gas dynamicsen
dc.subject.ddc519en
dc.titleRelaxation rate, diffusion approximation and Fick's law for inelastic scattering Boltzmann modelsen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUniversita degli studi di Pavia;Italie
dc.contributor.editoruniversityotherCNRS - Université Blaise Pascal -Clermont-Ferrand II;France
dc.description.abstractenWe consider the linear dissipative Boltzmann equation describing inelastic interactions of particles with a fixed background. For the simplified model of Maxwell molecules first, we give a complete spectral analysis, and deduce from it the optimal rate of exponential convergence to equilibrium. Moreover we show the convergence to the heat equation in the diffusive limit and compute explicitely the diffusivity. Then for the physical model of hard spheres we use a suitable entropy functional for which we prove explicit inequality between the relative entropy and the production of entropy to get exponential convergence to equilibrium with explicit rate. The proof is based on inequalities between the entropy production functional for hard spheres and Maxwell molecules. Mathematical proof of the convergence to some heat equation in the diffusive limit is also given. From the last two points we deduce the first explicit estimates on the diffusive coefficient in the Fick's law for (inelastic hard-spheres) dissipative gases.en
dc.relation.isversionofjnlnameKinetic and related models
dc.relation.isversionofjnlvol1en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate2008-06
dc.relation.isversionofjnlpages223-248en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00220504/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherAmerican Institute of Mathematical Sciences
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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