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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorLi, Xingyu
dc.date.accessioned2019-07-23T14:17:14Z
dc.date.available2019-07-23T14:17:14Z
dc.date.issued2019-06
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/19390
dc.language.isoenen
dc.subjectsymmetry breakingen
dc.subjectfree energyen
dc.subjectlarge time asymp- toticsen
dc.subjectFlocking modelen
dc.subjectphase transitionen
dc.subjectasymptotic rate of convergence AMS subject classificationsen
dc.subjectasymptotic rate of convergenceen
dc.subjectspectral gapen
dc.subjectstabilityen
dc.subject.ddc515en
dc.titleFlocking : Phase transition and asymptotic behaviouren
dc.typeDocument de travail / Working paper
dc.description.abstractenThis paper is devoted to a continuous Cucker-Smale model with noise, which has isotropic and polarized stationary solutions depending on the intensity of the noise. The first result establishes the threshold value of the noise parameter which drives the phase transition. This threshold value is used to classify all stationary solutions and their linear stability properties. Using an entropy, these stability properties are extended to the non-linear regime. The second result is concerned with the asymptotic behaviour of the solutions of the evolution problem. In several cases, we prove that stable solutions attract the other solutions with an optimal exponential rate of convergence determined by the spectral gap of the linearized problem around the stable solutions. The spectral gap has to be computed in a norm adapted to the non-local term.en
dc.publisher.nameCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages20en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-02143985en
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2019-06
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2019-07-23T14:11:00Z
hal.author.functionaut


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