A limiting absorption principle for scattering problems with unbounded obstacles
septembre, 2001
Type de publication :
Article (revues avec comité de lecture)
Journal :
Mathematical Methods in the Applied Sciences, vol. 24(14), pp. 1089--1111
DOI :
HAL :
Résumé :
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.
BibTeX :
@article{Bon-Til-2001-1,
author={Anne-Sophie Bonnet-BenDhia and Axel Tillequin },
title={A limiting absorption principle for scattering problems with
unbounded obstacles },
doi={10.1002/mma.259 },
journal={Mathematical Methods in the Applied Sciences },
year={2001 },
month={9},
volume={24(14) },
pages={1089--1111},
}