Null controllability of a nonlinear population dynamics problem

Abstract

We establish a null controllability result for a nonlinear population dynamics model. In our model, the birth term is nonlocal and describes the recruitment process in newborn individuals population. Using a derivation of Leray-Schauder fixed point theorem and Carleman inequality for the adjoint system, we show that for all given initial density, there exists an internal control acting on a small open set of the domain and leading the population to extinction.

Null controllability and application to data assimilation problem for a linear model of population dynamics

“…The proof of this Carleman inequality follows the method of [10] for parabolic equation. In [13] we have established similar Carleman inequality, but without the particular form of the constants.See also [2]. For completeness and in order to justify the particular form of the constants λ 0 and s 0 (λ) we give the entire proof in the appendix, at the end of the paper.…”

Controllability with Positivity Constraints of the Lotka--McKendrick System

“…Related approximate and exact controllability issues have also been studied in Ainseba [2], Ainseba and Langlais [5], Ainseba and Iannelli [4], Traore [24], Kavian and Traore [17]. Using a direct approach, the approximate controllability by birth or boundary control is studied in Yu, Guo and Zhu [27].…”

Boundary Null Controllability With Constrained Control for a Nonlinear Two Stroke System: Application to Boundary Sentinel and Identification of Parameters in a Nonlinear Population Dynamics Model

“…Concerning the nonlinear population dynamics model, a null controllability result was established by Ainseba, B. and Iannelli, M. by means of Kakutani fixed point theorem (Ainseba & Innanelli, 2003). Using a derivation of Leray-Schauder fixed point theorem and Carleman inequality for the adjoint system, Traoré, O. showed that for all given initial density, there exists an internal control acting on a small open set of the domain and leading the population to extension in (Traoré, 2006). Sawadogo, S. and Mophou, G. (Sawadogo & Mophou, 2012) gave a null controllability result for population dynamics model with constraints on the state when the age of the population belongs to (γ, A) for any γ > 0.…”