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dc.contributor.authorBonforte, Matteo
dc.contributor.authorDolbeault, Jean
dc.contributor.authorMuratori, Matteo
dc.contributor.authorNazaret, Bruno
dc.date.accessioned2017-11-27T11:46:08Z
dc.date.available2017-11-27T11:46:08Z
dc.date.issued2017
dc.identifier.issn1937-5093
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17059
dc.language.isoenen
dc.subjectHardy-Poincaré inequalities
dc.subjectfree energy
dc.subjectCaffarelli-Kohn-Nirenberg inequalities
dc.subjectweights
dc.subjectoptimal functions
dc.subjectbest constants
dc.subjectFast diffusion equation
dc.subjectself-similar solutions
dc.subjectasymptotic behavior
dc.subjectintermediate asymptotics
dc.subjectrate of convergence
dc.subjectentropy methods
dc.subjectsymmetry breaking
dc.subjectlinearization
dc.subjectspectral gap
dc.subjectHarnack inequality
dc.subjectparabolic regularity
dc.subject.ddc515en
dc.titleWeighted fast diffusion equations (Part II): Sharp asymptotic rates of convergence in relative error by entropy methods
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper is the second part of the study. In Part~I, self-similar solutions of a weighted fast diffusion equation (WFD) were related to optimal functions in a family of subcritical Caffarelli-Kohn-Nirenberg inequalities (CKN) applied to radially symmetric functions. For these inequalities, the linear instability (symmetry breaking) of the optimal radial solutions relies on the spectral properties of the linearized evolution operator. Symmetry breaking in (CKN) was also related to large-time asymptotics of (WFD), at formal level. A first purpose of Part~II is to give a rigorous justification of this point, that is, to determine the asymptotic rates of convergence of the solutions to (WFD) in the symmetry range of (CKN) as well as in the symmetry breaking range, and even in regimes beyond the supercritical exponent in (CKN). Global rates of convergence with respect to a free energy (or entropy) functional are also investigated, as well as uniform convergence to self-similar solutions in the strong sense of the relative error. Differences with large-time asymptotics of fast diffusion equations without weights will be emphasized.
dc.relation.isversionofjnlnameKinetic & Related Models
dc.relation.isversionofjnlvol10
dc.relation.isversionofjnlissue1
dc.relation.isversionofjnldate2017
dc.relation.isversionofjnlpages61-91
dc.relation.isversionofdoi10.3934/krm.2017003
dc.relation.isversionofjnlpublisherAmerican Institute of Mathematical Sciences
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-12-15T13:55:28Z
hal.person.labIds82433
hal.person.labIds60
hal.person.labIds222478
hal.person.labIds92163


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