1. Null controllability of a nonlinear age, space and two-sex structured population dynamics model
- Author
-
Yacouba Simporé and Oumar Traore
- Subjects
education.field_of_study ,Control and Optimization ,Applied Mathematics ,010102 general mathematics ,Null (mathematics) ,Population ,Zero (complex analysis) ,Fixed-point theorem ,Space (mathematics) ,01 natural sciences ,010101 applied mathematics ,Combinatorics ,Controllability ,Mathematics - Analysis of PDEs ,Schauder fixed point theorem ,Optimization and Control (math.OC) ,FOS: Mathematics ,Quantitative Biology::Populations and Evolution ,Observability ,0101 mathematics ,education ,Mathematics - Optimization and Control ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
In this paper, we study the null controllability of a nonlinear age, space and two-sex structured population dynamics model. This model is such that the nonlinearity and the couplage are at birth level. We consider a population with males and females and we are dealing with two cases of null controllability problems. The first problem is related to the total extinction, which means that, we estimate a time \begin{document}$ T $\end{document} to bring the male and female subpopulation density to zero. The second case concerns null controllability of male or female subpopulation. Since the absence of males or females in the population stops births; so, if we have the total extinction of the females at time \begin{document}$ T, $\end{document} and if \begin{document}$ A $\end{document} is the life span of the individuals, at time \begin{document}$ T+A $\end{document} one will get certainly the total extinction of the population. Our method uses first an observability inequality related to the adjoint of an auxiliary system, a null controllability of the linear auxiliary system, and after the Schauder's fixed point theorem.
- Published
- 2023