Null Controllability of a nonlinear age, space and two-sex structured population dynamics model

TL;DR

This paper investigates the null controllability of a complex nonlinear population model with age, space, and two sexes, aiming to determine control strategies for population extinction or subpopulation control.

Contribution

It introduces a novel approach combining observability inequalities, linear controllability, and fixed point theory to address nonlinear, coupled population control problems.

Findings

Established null controllability for total population extinction.

Achieved null controllability for male or female subpopulations.

Developed a method applicable to nonlinear coupled population models.

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 problem. The first problem is related to the total extinction, which means that, we estimate a time $T$ to bring the male and female subpopulation density to zero. The second case concerns null controllability of male or female subpopulation individuals. Here, So if $A$ is the life span of the individuals, at time $T+A$ one will get 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.