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dc.contributor.authorCampos Serrano, Juan
dc.contributor.authorDolbeault, Jean
dc.date.accessioned2013-10-31T08:42:39Z
dc.date.available2013-10-31T08:42:39Z
dc.date.issued2014
dc.identifier.issn0360-5302
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/11954
dc.language.isoenen
dc.subjectLyapunov functiona
dc.subjectspectral gap
dc.subjectrelative entropy
dc.subjectfree energy
dc.subjectself-similar solutions
dc.subjectlogarithmic Hardy-Littlewood-Sobolev inequality
dc.subjectsubcritical mass
dc.subjectlarge time asymptotics
dc.subjectchemotaxis
dc.subjectKeller-Segel model
dc.subject.ddc515en
dc.titleAsymptotic estimates for the parabolic-elliptic Keller-Segel model in the plane
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherDepartamento de Ingeniería Matemática [Santiago] (DIM) http://www.dim.uchile.cl Departamento de Ingeniería Matemática – Universidad de Chile;Chili
dc.description.abstractenWe investigate the large-time behavior of the solutions of the two-dimensional Keller-Segel system in self-similar variables, when the total mass is subcritical, that is less than 8π after a proper adimensionalization. It was known from previous works that all solutions converge to stationary solutions, with exponential rate when the mass is small. Here we remove this restriction and show that the rate of convergence measured in relative entropy is exponential for any mass in the subcritical range, and independent of the mass. The proof relies on symmetrization techniques, which are adapted from a paper of J.I. Diaz, T. Nagai, and J.-M. Rakotoson, and allow us to establish uniform estimates for Lp norms of the solution. Exponential convergence is obtained by the mean of a linearization in a space which is defined consistently with relative entropy estimates and in which the linearized evolution operator is self-adjoint. The core of proof relies on several new spectral gap estimates which are of independent interest.
dc.relation.isversionofjnlnameCommunications in Partial Differential Equations
dc.relation.isversionofjnlvol39
dc.relation.isversionofjnlissue5
dc.relation.isversionofjnldate2014
dc.relation.isversionofjnlpages806-841
dc.relation.isversionofdoihttp://dx.doi.org/10.1080/03605302.2014.885046
dc.relation.isversionofjnlpublisherMarcel Dekker
dc.subject.ddclabelAnalyseen
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-02-07T16:08:29Z


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