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Generalized principal eigenvalues of space-time periodic, weakly coupled, cooperative, parabolic systems

hal.structure.identifierInstitut Camille Jordan [ICJ]
dc.contributor.authorGirardin, Léo
HAL ID: 20905
ORCID: 0000-0001-8201-2053
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorMazari, Idriss
HAL ID: 751069
dc.date.accessioned2022-03-02T14:10:20Z
dc.date.available2022-03-02T14:10:20Z
dc.date.issued2021
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22853
dc.language.isoenen
dc.subjectprincipal eigenvaluesen
dc.subjectspace-time periodicityen
dc.subjectcooperative systemsen
dc.subject.ddc519en
dc.titleGeneralized principal eigenvalues of space-time periodic, weakly coupled, cooperative, parabolic systemsen
dc.typeDocument de travail / Working paper
dc.description.abstractenThis paper is concerned with generalizations of the notion of principal eigenvalue in the context of space-time periodic cooperative systems. When the spatial domain is the whole space, the Krein-Rutman theorem cannot be applied and this leads to more sophisticated constructions and to the notion of generalized principal eigenvalues. These are not unique in general and we focus on a one-parameter family corresponding to principal eigenfunctions that are space-time periodic multiplicative perturbations of exponentials of the space variable. Besides existence and uniqueness properties of such principal eigenpairs, we also prove various dependence and optimization results illustrating how known results in the scalar setting can, or cannot, be extended to the vector setting. We especially prove an optimization property on minimizers and maximizers among mutation operators valued in the set of bistochastic matrices that is, to the best of our knowledge, new.en
dc.publisher.cityParisen
dc.identifier.citationpages77en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris Dauphine-PSLen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-03349049en
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.identifier.citationdate2021
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2022-03-02T14:08:21Z
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