%0 Journal Article
%T A limiting absorption principle for scattering problems with unbounded obstacles
%+ Propagation des Ondes : Étude Mathématique et Simulation (POEMS)
%A Bonnet-Ben Dhia, Anne-Sophie
%A Tillequin, Axel
%< avec comité de lecture
%@ 0170-4214
%J Mathematical Methods in the Applied Sciences
%I Wiley
%V 24
%N 14
%P 1089--1111
%8 2001-09
%D 2001
%R 10.1002/mma.259Journal articles
%X 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.
%G English
%L hal-01008796
%U https://ensta-paris.hal.science/hal-01008796
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