Variational formulations for scattering in a three-dimensional acoustic waveguide

Arens, T; Gintides, D; Lechleiter, A

dc.contributor.author	Arens, T	en
dc.contributor.author	Gintides, D	en
dc.contributor.author	Lechleiter, A	en
dc.date.accessioned	2014-03-01T01:29:28Z
dc.date.available	2014-03-01T01:29:28Z
dc.date.issued	2008	en
dc.identifier.issn	0170-4214	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19271
dc.subject	Elliptic equations	en
dc.subject	Reduced wave equation (Helmholtz)	en
dc.subject	Variational methods for second order	en
dc.subject	Wave scattering	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Computational geometry	en
dc.subject.other	Modal analysis	en
dc.subject.other	Problem solving	en
dc.subject.other	Variational techniques	en
dc.subject.other	Wave equations	en
dc.subject.other	Elliptic equations	en
dc.subject.other	Garding inequality	en
dc.subject.other	Reduced wave equations	en
dc.subject.other	Wave scattering	en
dc.subject.other	Acoustic wave scattering	en
dc.title	Variational formulations for scattering in a three-dimensional acoustic waveguide	en
heal.type	journalArticle	en
heal.identifier.primary	10.1002/mma.947	en
heal.identifier.secondary	http://dx.doi.org/10.1002/mma.947	en
heal.language	English	en
heal.publicationDate	2008	en
heal.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 Garding 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 (C) 2007 John Wiley & Sons, Ltd.	en
heal.publisher	JOHN WILEY & SONS LTD	en
heal.journalName	Mathematical Methods in the Applied Sciences	en
dc.identifier.doi	10.1002/mma.947	en
dc.identifier.isi	ISI:000255080900005	en
dc.identifier.volume	31	en
dc.identifier.issue	7	en
dc.identifier.spage	821	en
dc.identifier.epage	847	en