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Sibirskii Matematicheskii Zhurnal, 2015, Volume 56, Number 4, Pages 732–751
DOI: https://doi.org/10.17377/smzh.2015.56.402 (Mi smj2674) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Gaps in the spectrum of a waveguide composed of domains with different limiting dimensions

F. L. Bakhareva, S. A. Nazarovabc

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg State Polytechnical University, St. Petersburg, Russia
c Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (382 kB) Citations (15)
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DOI: https://doi.org/10.17377/smzh.2015.56.402
Abstract: We consider an acoustic waveguide (the Neumann problem for the Helmholtz equation) shaped like a periodic family of identical beads on a thin cylinder rod. Under minor restrictions on the bead and rod geometry, we use asymptotic analysis to establish the opening of spectral gaps and find their geometric characteristics. The main technical difficulties lie in the justification of asymptotic formulas for the eigenvalues of the model problem on the periodicity cell due to its arbitrary shape.
Keywords: Neumann problem, junction of domains with different limiting dimensions, periodic waveguide, spectral gaps, asymptotics.
Received: 10.09.2014
English version:
Siberian Mathematical Journal, 2015, Volume 56, Issue 4, Pages 575–592
DOI: https://doi.org/10.1134/S0037446615040023
Bibliographic databases:
Document Type: Article
UDC: 517.956.8+517.956.328+517.958+535.4
Language: Russian
Citation: F. L. Bakharev, S. A. Nazarov, “Gaps in the spectrum of a waveguide composed of domains with different limiting dimensions”, Sibirsk. Mat. Zh., 56:4 (2015), 732–751; Siberian Math. J., 56:4 (2015), 575–592
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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