MAITY, Debayan; TUCSNAK, Marius; ZUAZUA, Enrique

doi:10.1016/j.matpur.2018.12.006

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MAITY, Debayan
Institut de Mathématiques de Bordeaux [IMB]

TUCSNAK, Marius
Institut de Mathématiques de Bordeaux [IMB]

ZUAZUA, Enrique
Departamento de Matematicas [Madrid]
Universidad de Deusto [DEUSTO]

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Article de revue

Ce document a été publié dans

Journal de Mathématiques Pures et Appliquées. 2018

Elsevier

Date de soutenance

2018

Résumé en anglais

In 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.< Réduire

Mots clés en anglais

Population dynamics

Null controllability

URI

https://oskar-bordeaux.fr/handle/20.500.12278/193208

DOI

http://dx.doi.org/10.1016/j.matpur.2018.12.006

Project ANR

Systèmes interconnectés de dimension infinie pour les milieux hétérogènes - ANR-16-CE92-0028

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251