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Problèmes aux limites, optique géométrique et singularités

Abstract : We are interested in hyperbolic boundary value problems in the half space or in the quarter space. This manuscript is composed of two independant parts, the first one deals with weakly well-posed problems in the half space. By weakly well-posed we mean that the solution is not as regular as the source terms of the problem. In this framework, we show the optimality of energy estimates established in the existing literature and a finite speed of propagation result. In the second part of the manuscript, about hyperbolic boundary value problems in the quarter space, we show that the problem is strongly well-posed (in the sense that the solution is as regular as the source terms) in the particular framework of symetric with stricly dissipative boundary conditions problems. Then we give some new contributions about the strong well-posedness in the general framework. Finally, we construct rigorous geometric optics expansion of the solution of the problem in the quarter space. This expansion permits, in particular, to show that some new phenomenons such that selfinteraction phenomenons beetwen the phases, the generation of an infinite number of phases or the concentration at the corner.
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https://tel.archives-ouvertes.fr/tel-01180449
Contributor : Antoine Benoit <>
Submitted on : Monday, July 27, 2015 - 10:46:23 AM
Last modification on : Tuesday, September 21, 2021 - 4:06:02 PM

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Antoine Benoit. Problèmes aux limites, optique géométrique et singularités. Equations aux dérivées partielles [math.AP]. Université de Nantes, 2015. Français. ⟨tel-01180449⟩

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