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On the null controllability of the Lotka-Mckendrick system

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

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  • 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.

    Mathematics Subject Classification: 93B03, 93B05, 92D25.

    Citation:

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  • Figure 1.  Minimal time required for observability inequality to hold for the transport equation. For both cases, $ \widetilde q(T, \cdot) = 0 $ on the purple region

    Figure 2.  An illustration of estimate of $ q(t, 0) $ with $ a_{2} = a_{b}. $

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