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dc.contributor.authorFernandez, Javier
dc.contributor.authorEscobedo, Miguel
dc.contributor.authorDolbeault, Jean
dc.contributor.authorBlanchet, Adrien
dc.date.accessioned2010-01-27T10:59:41Z
dc.date.available2010-01-27T10:59:41Z
dc.date.issued2010
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3164
dc.language.isoenen
dc.subjectIntermediate Asymptoticsen
dc.subjectSelf-similar Solutionen
dc.subjectDrift-diffusionen
dc.subjectChemotaxisen
dc.subjectKeller-Segel Modelen
dc.subjectEntropyen
dc.subjectFree Energyen
dc.subjectRate of Convergenceen
dc.subjectHeat Kernelen
dc.subject.ddc515en
dc.titleAsymptotic behaviour for small mass in the two-dimensional parabolic-elliptic Keller-Segel modelen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUniversidad Publica de Navarra;Espagne
dc.contributor.editoruniversityotherUniversité des Sciences Sociales Toulouse 1;France
dc.contributor.editoruniversityotherUniversidad del Pais Vasco;Espagne
dc.description.abstractenThe Keller-Segel system describes the collective motion of cells that are attracted by a chemical substance and are able to emit it. In its simplest form, it is a conservative drift-diffusion equation for the cell density coupled to an elliptic equation for the chemo-attractant concentration. This paper deals with the rate of convergence towards a unique stationary state in self-similar variables, which describes the intermediate asymptotics of the solutions in the original variables. Although it is known that solutions globally exist for any mass less $8\pi\,$, a smaller mass condition is needed in our approach for proving an exponential rate of convergence in self-similar~variables.en
dc.relation.isversionofjnlnameJournal of Mathematical Analysis and Applications
dc.relation.isversionofjnlvol361en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate2010-01
dc.relation.isversionofjnlpages533-542en
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.jmaa.2009.07.034en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00349216/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelAnalyseen


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