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Variational formulations for scattering in a three-dimensional acoustic waveguide

✍ Scribed by Tilo Arens; Drossos Gintides; Armin Lechleiter

Publisher: John Wiley and Sons
Year: 2008
Tongue: English
Weight: 282 KB
Volume: 31
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.947

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✦ Synopsis

Abstract

Variational formulations for direct time‐harmonic scattering problems in a three‐dimensional waveguide are formulated and analyzed. We prove that the operators defined by the corresponding forms satisfy a Gårding inequality in adequately chosen spaces of test and trial functions and depend analytically on the wavenumber except at the modal numbers of the waveguide. It is also shown that these operators are strictly coercive if the wavenumber is small enough. It follows that these scattering problems are uniquely solvable except possibly for an infinite series of exceptional values of the wavenumber with no finite accumulation point. Furthermore, two geometric conditions for an obstacle are given, under which uniqueness of solution always holds in the case of a Dirichlet problem. Copyright © 2007 John Wiley & Sons, Ltd.

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