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Méthodes de factorisation des équations aux dérivées partielles.

Isabelle Champagne 1
1 ONDES - Modeling, analysis and simulation of wave propagation phenomena
Inria Paris-Rocquencourt, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR2706
Abstract : This thesis aims at giving a new means of studying the Helmholtz problem inwaveguides. Our method is based on invariant embedding for cylindrical domains: a family of problems, which are similar to the initial one but take place in subdomains, is introduced. This enables us to factorize the Helmholtz equation and to get a decoupled system of differential equations. One of these is a Riccati equation and its solution is a first order differential operator - usually a Dirichlet-to-Neumann one. A representation formula for this solution is then given: introducing a homographic transformation enables us to prove it is similar to a linear semigroup.
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Isabelle Champagne. Méthodes de factorisation des équations aux dérivées partielles.. Equations aux dérivées partielles [math.AP]. Ecole Polytechnique X, 2004. Français. ⟨pastel-00000920⟩

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