Contrôlabilité exacte d'équations dispersives issues de la mécanique.

Abstract : In this thesis, we study the exact controllability of two dispersive equations, the Korteweg-de Vries equation and the "good" Boussinesq equation. First, for the Korteweg-de Vries equation, we extend a result of Rosier. We prove that for a critical length, the nonlinear equation is exactly controllable in a neighborhood of a small non null stationary solution. This study uses the Hilbert Uniqueness Method with the multiplier theory and a fixed point theorem. Secondly, we study the exact controllability of the "good" Boussinesq equation with two different boundary controls. We use again the Hilbert Uniqueness Method but with Ingham inequality. Lastly, we apply this method for a numerical approach of the controllability of the Boussinesq equation both for linear and nonlinear equations. The control is applied to the second spatial derivative, at the right endpoint.
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Contributor : Emmanuelle Crepeau <>
Submitted on : Friday, October 24, 2003 - 9:43:28 AM
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Emmanuelle Crépeau. Contrôlabilité exacte d'équations dispersives issues de la mécanique.. Mathématiques [math]. Université Paris Sud - Paris XI, 2002. Français. ⟨tel-00003637⟩

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