Null controllability of the Lotka-McKendrick system with spatial diffusion

Nicolas Hegoburu (1) , Marius Tucsnak (1)

1 IMB - Institut de Mathématiques de Bordeaux

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.

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Nicolas Hegoburu, Marius Tucsnak. Null controllability of the Lotka-McKendrick system with spatial diffusion. Mathematical Control and Related Fields, 2018, 8 (3-4), pp.707-720. ⟨hal-01648088⟩