Time optimal internal controls for the Lotka-McKendrick equation with spatial diffusion

Nicolas Hegoburu (1)

1 IMB - Institut de Mathématiques de Bordeaux

This work is devoted to establish a bang-bang principle of time optimal controls for a controlled age-structured population evolving in a bounded domain of R^n. Here, the bang-bang principle is deduced by an L^∞ null-controllability result for the Lotka-McKendrick equation with spatial diffusion. This L^∞ null-controllability result is obtained by combining a methodology employed by Hegoburu and Tucsnak-originally devoted to study the null-controllability of the Lotka-McKendrick equation with spatial diffusion in the more classical L^2 setting-with a strategy developed by Wang, originally intended to study the time optimal internal controls for the heat equation.

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

Nicolas Hegoburu. Time optimal internal controls for the Lotka-McKendrick equation with spatial diffusion. Mathematical Control and Related Fields, 2019, 9 (4), pp.697-718. ⟨hal-01925980⟩