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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorMischler, Stéphane
hal.structure.identifierLaboratoire Jacques-Louis Lions [LJLL]
dc.contributor.authorQuiñinao, Cristóbal
hal.structure.identifierLaboratory of Mathematical Physics
hal.structure.identifierCentre interdisciplinaire de recherche en biologie [CIRB]
hal.structure.identifierLabex MemoLife
dc.contributor.authorTouboul, Jonathan
dc.date.accessioned2018-02-19T14:33:30Z
dc.date.available2018-02-19T14:33:30Z
dc.date.issued2016
dc.identifier.issn0010-3616
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17422
dc.language.isoenen
dc.subjectBanach Spaceen
dc.subjectPeriodic Solutionen
dc.subjectStationary Solutionen
dc.subjectNeuronal Networken
dc.subjectBanach Latticeen
dc.subject.ddc515en
dc.titleOn a Kinetic Fitzhugh–Nagumo Model of Neuronal Networken
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe investigate existence and uniqueness of solutions of a McKean-Vlasov evolution PDE representing the macroscopic behaviour of interacting Fitzhugh-Nagumo neurons. This equation is hypoelliptic , nonlocal and has unbounded coefficients. We prove existence of a solution to the evolution equation and non trivial stationary solutions. Moreover , we demonstrate uniqueness of the stationary solution in the weakly nonlinear regime. Eventually , using a semi-group factorisation method , we show exponential nonlinear stability in the small connectivity regime .en
dc.relation.isversionofjnlnameCommunications in Mathematical Physics
dc.relation.isversionofjnlvol342en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2016
dc.relation.isversionofjnlpages1001–1042en
dc.relation.isversionofdoi10.1007/s00220-015-2556-9en
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2018-02-19T14:13:05Z
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