Etude de quelques problèmes de contrôlabilité exacte et de stabilisation dépendant ou non de petits paramètres

Abstract : This thesis is constituted by different results of exact controllability and stabilization ; it is divided into five chapters. In the first two chapters, we use the hilbert uniqueness method of J.L. Lions to study the exact internal controllability of the wave equation in perturbed domains. In the third chapter, we study the internal stabilization of the vibrations of a structure which looks like a grid and we use the principle of D.L. Russell to deduce from that the exact controllability of these vibrations. The fourth chapter is based on a result of J.L. Lions in the theory of exact controllability of plates an singular perturbations; in this chapter, we solve an open problem which is in the second volume of his monograph on exact controllability. In the fifth and last chapter, we work in two-dimensional domains; we prove that a judicious choice of feedback provides a better stabilization result for the wave equation than a previous result of V. Komornik. We also study the stabilization of the linear system of elasticity
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Louis Roder Tcheugoué Tébou. Etude de quelques problèmes de contrôlabilité exacte et de stabilisation dépendant ou non de petits paramètres. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1995. Français. ⟨NNT : 1995METZ013S⟩. ⟨tel-01776912⟩

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