# American Institute of Mathematical Sciences

December  2019, 9(4): 719-728. doi: 10.3934/mcrf.2019048

## On the null controllability of the Lotka-Mckendrick system

 Institut de Mathématiques, Université de Bordeaux, Bordeaux INP, CNRS F-33400 Talence, France

Received  January 2019 Revised  May 2019 Published  November 2019

Fund Project: Debayan Maity acknowledges the support of the Agence Nationale de la Recherche - Deutsche Forschungsgemeinschaft (ANR - DFG), project INFIDHEM, ID ANR-16-CE92-0028.

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.

Citation: Debayan Maity. On the null controllability of the Lotka-Mckendrick system. Mathematical Control & Related Fields, 2019, 9 (4) : 719-728. doi: 10.3934/mcrf.2019048
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##### References:
Minimal time required for observability inequality to hold for the transport equation. For both cases, $\widetilde q(T, \cdot) = 0$ on the purple region
An illustration of estimate of $q(t, 0)$ with $a_{2} = a_{b}.$