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Theses

Problèmes de contrôle et équations hyperboliques non-linéaires

Abstract : In this thesis, we study some problems from control theory on several models from fluid mechanics.\par In chapter one, we study the Camassa-Holm equation on a compact interval. After introducing our boundary conditions and a notion of weak solution, we prove an existence result and a weak-strong uniqueness result for the non-homogeneous initial boundary value problem. In a second part, we establish a result on the global asymptotic stabilization problem by means of a boundary feedback law. In chapter two, we study the exact controllability problem for a 1-D scalar conservation law with convex flux, on a compact interval and in the context of entropy solution. We provide several sufficient conditions for a BV function to be reachable in any time and from any initial data in BV. We control the equation by means of the boundary data and also through a source term acting uniformly in space.\par Finally in chapter three, we investigate the asymptotic stabilization problem of the constant stationary solutions of a scalar conservation laws with a convex flux, on a compact interval and in the context of entropy solutions. Once again we control the equation through the boundary data and a source term acting uniformly in space. We provide two stationary feedback laws (depending on whether the state to stabilize has critical speed or not) which allow us to prove the global asymptotic stabilization property.
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https://tel.archives-ouvertes.fr/tel-00872271
Contributor : Vincent Perrollaz <>
Submitted on : Friday, October 11, 2013 - 3:29:48 PM
Last modification on : Monday, December 14, 2020 - 9:55:40 AM
Long-term archiving on: : Sunday, January 12, 2014 - 4:36:42 AM

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  • HAL Id : tel-00872271, version 1

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Perrollaz Vincent. Problèmes de contrôle et équations hyperboliques non-linéaires. Equations aux dérivées partielles [math.AP]. Université Pierre et Marie Curie - Paris VI, 2011. Français. ⟨tel-00872271⟩

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