Controllability and Positivity Constraints in Population Dynamics with Age Structuring and Diffusion
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MAITY, Debayan | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | TUCSNAK, Marius | |
| hal.structure.identifier | Departamento de Matematicas [Madrid] | |
| hal.structure.identifier | Universidad de Deusto [DEUSTO] | |
| dc.contributor.author | ZUAZUA, Enrique | |
| dc.date | 2018 | |
| dc.date.accessioned | 2024-04-04T03:05:01Z | |
| dc.date.available | 2024-04-04T03:05:01Z | |
| dc.date.issued | 2018 | |
| dc.identifier.issn | 0021-7824 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193208 | |
| dc.description.abstractEn | 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. | |
| dc.description.sponsorship | Systèmes interconnectés de dimension infinie pour les milieux hétérogènes - ANR-16-CE92-0028 | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | Population dynamics | |
| dc.subject.en | Null controllability | |
| dc.title.en | Controllability and Positivity Constraints in Population Dynamics with Age Structuring and Diffusion | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.matpur.2018.12.006 | |
| dc.subject.hal | Mathématiques [math]/Optimisation et contrôle [math.OC] | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.journal | Journal de Mathématiques Pures et Appliquées | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01764865 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01764865v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20de%20Math%C3%A9matiques%20Pures%20et%20Appliqu%C3%A9es&rft.date=2018&rft.eissn=0021-7824&rft.issn=0021-7824&rft.au=MAITY,%20Debayan&TUCSNAK,%20Marius&ZUAZUA,%20Enrique&rft.genre=article |
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