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Habilitation à diriger des recherches

Méthodes fonctionnelles et numériques pour l'approche de problèmes aux limites non linéaires mixtes elliptiques / hyperboliques

Abstract : Works presented in this report in order to obtain an HDR concern nonlinear boundary value problems of mixed type elliptic / hyperbolic. We also take into account an inequality constraint. Here we present the significant case of the boundary value problem issued from the Karman and Guderley model with entropic condition. The advantage of this problem is the simplicity of its description. Nevertheless, it contains a nonlinear term involving principal difficulties of nonlinear problems of mixed type. This boundary value problem is ill posed : functional spaces assuming existence or uniqueness of the solution doesn't exist. Our aim is to present a analysis method assuming coherence between functional and numerical results. First, the boundary value problem is considered without taking into account entropic condition. Using variational formulation and generalized Green formula, we transform the problem : we have now to annul an adapted projection. Introducing adapted norm, we minimize a criterion. Then, we consider the entropic condition. The constraint is also modified by the generalized Green formula : the inequality constraint is transformed in an equality one. A penalized criterion is minimized.
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Habilitation à diriger des recherches
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https://tel.archives-ouvertes.fr/tel-00005350
Contributor : Jean-Sébastien Le Brizaut <>
Submitted on : Tuesday, April 27, 2004 - 8:04:32 AM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
Long-term archiving on: : Friday, April 2, 2010 - 7:36:56 PM

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Jean-Sébastien Le Brizaut. Méthodes fonctionnelles et numériques pour l'approche de problèmes aux limites non linéaires mixtes elliptiques / hyperboliques. Mathématiques [math]. Université de Nantes, 2004. ⟨tel-00005350⟩

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