Inverse scattering of elastic waves by periodic structures : uniqueness under the third or fourth kind boundary conditions

dc.bibliographicCitation.seriesTitleWIAS Preprintseng
dc.bibliographicCitation.volume1528
dc.contributor.authorElschner, Johannes
dc.contributor.authorHu, Guanghui
dc.date.accessioned2016-03-24T17:38:38Z
dc.date.available2019-06-28T08:05:33Z
dc.date.issued2010
dc.description.abstractThe inverse scattering of a time-harmonic elastic wave by a two-dimensional periodic structure in R 2 is investigated. The grating profile is assumed to be a graph given by a piecewise linear function on which the third or fourth kind boundary conditions are satisfied. Via an equivalent variational formulation, existence of quasi-periodic solutions for general Lipschitz grating profiles is proved by applying the Fredholm alternative. However, uniqueness of solution to the direct problem does not hold in general. For the inverse problem, we determine and classify all the unidentifiable grating profiles corresponding to a given incident elastic field, relying on the reflection principle for the Navier equation and the rotational invariance of propagating directions of the total field. Moreover, global uniqueness for the inverse problem is established with a minimal number of incident pressure or shear waves, including the resonance case where a Rayleigh frequency is allowed. The gratings that are unidentifiable by one incident elastic wave provide non-uniqueness examples for appropriately chosen wave number and incident angleseng
dc.description.versionpublishedVersioneng
dc.formatapplication/pdf
dc.identifier.issn0946-8633
dc.identifier.urihttps://doi.org/10.34657/2568
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/2319
dc.language.isoengeng
dc.publisherBerlin : Weierstraß-Institut für Angewandte Analysis und Stochastikeng
dc.relation.issn0946-8633eng
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.eng
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.ger
dc.subject.ddc510eng
dc.subject.otherDiffraction gratingseng
dc.subject.otherinverse scatteringeng
dc.subject.otheruniquenesseng
dc.subject.otherelastic waveseng
dc.titleInverse scattering of elastic waves by periodic structures : uniqueness under the third or fourth kind boundary conditionseng
dc.typeReporteng
dc.typeTexteng
tib.accessRightsopenAccesseng
wgl.contributorWIASeng
wgl.subjectMathematikeng
wgl.typeReport / Forschungsbericht / Arbeitspapiereng
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