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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMAITY, Debayan
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorTUCSNAK, Marius
hal.structure.identifierDepartamento de Matematicas [Madrid]
hal.structure.identifierUniversidad de Deusto [DEUSTO]
dc.contributor.authorZUAZUA, Enrique
dc.date2018
dc.date.accessioned2024-04-04T03:05:01Z
dc.date.available2024-04-04T03:05:01Z
dc.date.issued2018
dc.identifier.issn0021-7824
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193208
dc.description.abstractEnIn this article, we study the null controllability of a linear system coming from a population dynamics model with age structuring and spatial diffusion (of Lotka-McKendrick type). The control is localized in the space variable as well as with respect to the age. The first novelty we bring in is that the age interval in which the control needs to be active can be arbitrarily small and does not need to contain a neighbourhood of 0. The second one is that we prove that the whole population can be steered into zero in a uniform time, without, as in the existing literature, excluding some interval of low ages. Moreover, we improve the existing estimates of the controllability time and we show that our estimates are sharp, at least when the control is active for very low ages. Finally, we show that the system can be steered between two positive steady states by controls preserving the positivity of the state trajectory. The method of proof, combining final-state observability estimates with the use of characteristics and with $L^\infty$ estimates of the associated semigroup, avoids the explicit use of parabolic Carleman estimates.
dc.description.sponsorshipSystèmes interconnectés de dimension infinie pour les milieux hétérogènes - ANR-16-CE92-0028
dc.language.isoen
dc.publisherElsevier
dc.subject.enPopulation dynamics
dc.subject.enNull controllability
dc.title.enControllability and Positivity Constraints in Population Dynamics with Age Structuring and Diffusion
dc.typeArticle de revue
dc.identifier.doi10.1016/j.matpur.2018.12.006
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.journalJournal de Mathématiques Pures et Appliquées
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01764865
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01764865v1
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