Abstract
In this work, we study null-controllability of the Lotka-McKendrick system of population dynamics. The control is acting on the individuals in a given age range. The main novelty we bring in this work is that the age interval in which the control is active does not necessarily contain a neighbourhood of $ 0. $ The main result asserts the whole population can be steered into zero in large time. The proof is based on final-state observability estimates of the adjoint system with the use of characteristics.
Highlights
We study the null-controllability of an infinite dimensional linear system describing the dynamics of an age-structured single species population
We study null-controllability of the classical Lotka-McKendrick system
Hegoburu, Magal and Tucsnak [5] considered the system (1.1) with distributed control supported in (0, a2). They proved that the restriction of [4] is unnecessary, i.e., the whole population can be steered into a steady state, provided the individuals do not reproduce at the age near zero
Summary
On the Null Controllability of the Lotka-Mckendrick System. Mathematical Control and Related Fields, AIMS, 2019, 10.3934/mcrf.2019048. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés
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