Controllability of a Class of Infinite Dimensional Systems With Age Structure.

Debayan Maity (1) , Marius Tucsnak (2) , Enrique Zuazua (1, 3)

1 UAM - Universidad Autónoma de Madrid
2 IMB - Institut de Mathématiques de Bordeaux
3 DEUSTO - Universidad de Deusto

Given a linear dynamical system, we investigate the linear infinite dimensional system obtained by grafting an age structure. Such systems appear essentially in population dynamics with age structure when phenomena like spatial diffusion or transport are also taken into consideration. We first show that the new system preserves some of the wellposedness properties of the initial one. Our main result asserts that if the initial system is null controllable in a time small enough than the structured system is also null controllable in a time depending on the various involved parameters.

Mots clés: Infinite dimensional linear system; age structure; admissible control operator; null controllability; population dynamics; null controlla- bility; population dynamics AMS subject classifications 93B03; 93B05; 92D25

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

Debayan Maity, Marius Tucsnak, Enrique Zuazua. Controllability of a Class of Infinite Dimensional Systems With Age Structure.. Control and Cybernetics, In press. ⟨hal-01964612v2⟩