Title : A limiting absorption principle for scattering problems with unbounded obstacles
Year : 2001
Type : paper in peer-reviewed journal
Authors : A.-S. Bonnet-BenDhia, A. Tillequin
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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Reference : Mathematical Methods in the Applied Sciences - vol. 24(14) (pp 1089--1111 )