A limiting absorption principle for scattering problems with unbounded obstacles

Anne-Sophie Bonnet-Ben Dhia 1 Axel Tillequin
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, ENSTA ParisTech UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : A generalized mode matching method that applies to a wide class of scattering problems is developed in the time harmonic two-dimensional Helmholtz case. This method leads by variational means to an integro-differential formulation whose unknown is the trace of the field on an unbounded one-dimensional interface. The well-posedness is proved after a careful study of the rather original functional framework. Owing to a fundamental density result--based upon some properties of a singular integral operator similar to the Hilbert transform--the limiting absorption principle related to this original formulation is established. Finally, two other situations are emphasized. Copyright © 2001 John Wiley & Sons, Ltd.
Type de document :
Article dans une revue
Mathematical Methods in the Applied Sciences, Wiley, 2001, 24 (14), pp.1089--1111. <10.1002/mma.259>
Liste complète des métadonnées

https://hal-ensta.archives-ouvertes.fr/hal-01008796
Contributeur : Aurélien Arnoux <>
Soumis le : mardi 17 juin 2014 - 11:52:21
Dernière modification le : jeudi 9 février 2017 - 15:28:14

Identifiants

Collections

Citation

Anne-Sophie Bonnet-Ben Dhia, Axel Tillequin. A limiting absorption principle for scattering problems with unbounded obstacles. Mathematical Methods in the Applied Sciences, Wiley, 2001, 24 (14), pp.1089--1111. <10.1002/mma.259>. <hal-01008796>

Partager

Métriques

Consultations de la notice

105