# American Institute of Mathematical Sciences

September  2018, 8(3&4): 707-720. doi: 10.3934/mcrf.2018030

## Null controllability of the Lotka-McKendrick system with spatial diffusion

 1 Institut de Mathématiques de Bordeaux, Université de Bordeaux/Bordeaux INP/CNRS, 351 Cours de la Libération, 33 405 Talence, France 2 Institut de Mathématiques de Bordeaux UMR 5251, Université de Bordeaux/Bordeaux INP/CNRS, 351 Cours de la Libération, 33 405 Talence, France

* Corresponding author: Marius Tucsnak

Received  November 2017 Revised  May 2018 Published  September 2018

We consider the infinite dimensional linear control system described by the population dynamics model of Lotka-McKendrick with spatial diffusion. Considering control functions localized with respect to the spatial variable but active for all ages, we prove that the whole population can be steered to zero in any positive time. The main novelty we bring is that, unlike the existing results in the literature, we can also control the population of ages very close to 0. Another novelty brought in is the employed methodology: as far as we know, the present work is the first one remarking that the null controllability of the considered system can be obtained by using the Lebeau-Robbiano strategy, originally developed for the null-controllability of the heat equation.

Citation: Nicolas Hegoburu, Marius Tucsnak. Null controllability of the Lotka-McKendrick system with spatial diffusion. Mathematical Control & Related Fields, 2018, 8 (3&4) : 707-720. doi: 10.3934/mcrf.2018030
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##### References:
The spectrum of the free diffusion operator $A_0$ (green crosses) and of $-\Delta$ (red circles)
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