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Algebra i Analiz, 2009, Volume 21, Issue 2, Pages 166–204 (Mi aa1009)  

This article is cited in 3 scientific papers (total in 3 papers)

Opening a gap in the essential spectrum of the elasticity problem in a periodic semi-layer

S. A. Nazarov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

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 at most discrete spectrum.

Keywords: Rayleigh waves, essential spectrum, band structure.

Full text: PDF file (464 kB)
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English version:
St. Petersburg Mathematical Journal, 2010, 21:2, 281–307

Bibliographic databases:

MSC: 35Q72
Received: 08.05.2008

Citation: S. A. Nazarov, “Opening a gap in the essential spectrum of the elasticity problem in a periodic semi-layer”, Algebra i Analiz, 21:2 (2009), 166–204; St. Petersburg Math. J., 21:2 (2010), 281–307

Citation in format AMSBIB
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\paper Opening a~gap in the essential spectrum of the elasticity problem in a~periodic semi-layer
\jour Algebra i Analiz
\yr 2009
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\pages 166--204
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\jour St. Petersburg Math. J.
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\pages 281--307
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Nazarov, “An example of multiple gaps in the spectrum of a periodic waveguide”, Sb. Math., 201:4 (2010), 569–594  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Nazarov S.A., Ruotsalainen K., Taskinen J., “Essential spectrum of a periodic elastic waveguide may contain arbitrarily many gaps”, Appl. Anal., 89:1 (2010), 109–124  crossref  mathscinet  zmath  isi  elib  scopus
    3. Bakharev F.L., Taskinen J., “Bands in the Spectrum of a Periodic Elastic Waveguide”, Z. Angew. Math. Phys., 68:5 (2017), 102  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и анализ St. Petersburg Mathematical Journal
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