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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

Gap opening in the essential spectrum of the elasticity theory problem in a periodic half-layer


Author: S. A. Nazarov
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 21 (2009), nomer 2.
Journal: St. Petersburg Math. J. 21 (2010), 281-307
MSC (2000): Primary 35Q72
DOI: https://doi.org/10.1090/S1061-0022-10-01095-2
Published electronically: January 26, 2010
MathSciNet review: 2553046
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Abstract: Rayleigh waves are studied in an elastic half-layer with a periodic end and rigidly clamped faces. It is established that the essential spectrum of the corresponding problem of elasticity theory has a band structure, and an example of a waveguide is presented in which a gap opens in the essential spectrum; i.e., an interval arises that contains points of an at most discrete spectrum.


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Additional Information

S. A. Nazarov
Affiliation: Institute of Engineering Problems, Russian Academy of Sciences, 61 Bol’shoi Prospekt V.O., St. Petersburg 199178, Russia
Email: serna@snark.ipme.ru, srgnazarov@yahoo.co.uk

DOI: https://doi.org/10.1090/S1061-0022-10-01095-2
Keywords: Rayleigh waves, essential spectrum, band structure
Received by editor(s): May 8, 2008
Published electronically: January 26, 2010
Additional Notes: Supported by the Netherlands Organization for Scientific Research (NWO) and RFBR, joint project 047.017.020
Article copyright: © Copyright 2010 American Mathematical Society