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Méthodes d'analyse fonctionnelle pour des systèmes de dimension infinie issus de la dynamique de populations

Abstract : This work is devoted to study the controllability properties of some infinite dimensional systems modeling an age structured population dynamics. The considered equations are essentially those described by Lotka and McKendrick, with or without spatial diffusion, and their nonlinear versions described by the Gurtin and MacCamy equations. The first part of this thesis aims to study the controllability properties of the linear Lotka and McKendrick system (without diffusion), in the case when the control acts for the very young individuals. The null controllability and the controllability towards the stationnary solutions of the considered system are established, using a semigroup approach. In addition, the nonnegativity of the controlled population dynamics is studied. The next two parts are respectively devoted to establish a null controllability result and a time optimal control result for the Lotka McKendrick equation with spatial diffusion (here, the control acts for every ages but only on a subdomain of the considered spatial domain). The methods employed are those originally devoted to study the internal controllability properties of the heat equation. A last part studies the controllability properties of the Gurtin and MacCamy nonlinear equations (without diffuion), when the control acts only in an arbitrary age range. In this case, the use of comparison principles in age structured population dynamics ensures the null controllability of the considered equations.
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Submitted on : Friday, May 17, 2019 - 5:57:06 PM
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Nicolas Hegoburu. Méthodes d'analyse fonctionnelle pour des systèmes de dimension infinie issus de la dynamique de populations. Equations aux dérivées partielles [math.AP]. Université de Bordeaux, 2019. Français. ⟨NNT : 2019BORD0061⟩. ⟨tel-02133006⟩

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