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Examples of embedded eigenvalues for problems in acoustic waveguides

✍ Scribed by M. D. Groves

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 248 KB
Volume: 21
Category: Article
ISSN: 0170-4214
DOI: 10.1002/(sici)1099-1476(199804)21:6<479::aid-mma950>3.0.co;2-v

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✦ Synopsis

Communicated by P. Werner

This short article discusses the spectrum of the Neumann Laplacian in the infinite domain L1L, n*2 created by inserting a compact obstacle P into the uniform cylinder "( !R, R); . The main result is the existence of at least one embedded eigenvalue when P is an (n!2)-dimensional surface whose unit normal is parallel to at each point of P. The special case when P is symmetric about +0,; is also treated. It is shown that there is at least one symmetric eigenvector and, when P is sufficiently long, at least one antisymmetric eigenvector.

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