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

Abstract

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 \begin{document}$ \mathbb{R}^n $\end{document} . Here, the bang-bang principle is deduced by an \begin{document}$ L^\infty $\end{document} null-controllability result for the Lotka-McKendrick equation with spatial diffusion. This \begin{document}$ L^\infty $\end{document} null-controllability result is obtained by combining a methodology employed by Hegoburu and Tucsnak - originally devoted to study the null-controllability of the Lotka-McKendrick equation with spatial diffusion in the more classical \begin{document}$ L^2 $\end{document} setting - with a strategy developed by Wang, originally intended to study the time optimal internal controls for the heat equation.