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Null controllability via comparison results for nonlinear age-structured population dynamics

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Abstract

We consider an infinite dimensional nonlinear controlled system describing age-structured population dynamics, where the birth and the mortality rates are nonlinear functions of the population size. The control being active on some age range, we give sharp conditions subject to the age range and the control time horizon to get the null controllability of the nonlinear controlled population dynamics. The main novelty is that we use here as a main ingredient the comparison principle for age-structured population dynamics, and in case of null controllability we provide a feedback control with a very simple structure, while preserving the nonnegativity of the state trajectory. Finally, we establish the lack of the null controllability for the linear Lotka-McKendrick equation with spatial diffusion when the control acts in a subset of the habitat and we want to preserve the positivity of the state trajectory.

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Acknowledgements

Thanks are due to the Anonymous Referees for their precious advices and suggestions.

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Authors and Affiliations

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

    Nicolas Hegoburu

  2. Faculty of Mathematics, “Alexandru Ioan Cuza” University of Iaşi, Iaşi, Romania

    Sebastian Aniţa

  3. “Octav Mayer” Institute of Mathematics of the Romanian Academy, 700506, Iaşi, Romania

    Sebastian Aniţa

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  1. Nicolas Hegoburu
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  2. Sebastian Aniţa
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Correspondence to Nicolas Hegoburu.

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Hegoburu, N., Aniţa, S. Null controllability via comparison results for nonlinear age-structured population dynamics. Math. Control Signals Syst. 31, 2 (2019). https://doi.org/10.1007/s00498-019-0232-x

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