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, 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.
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Submitted on : Tuesday, June 17, 2014 - 11:52:21 AM
Last modification on : Wednesday, July 3, 2019 - 10:48:03 AM

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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⟩

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