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Sibirsk. Mat. Zh., 2015, Volume 56, Number 4, Pages 732–751 (Mi smj2674)  

This article is cited in 7 scientific papers (total in 7 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

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.

DOI: https://doi.org/10.17377/smzh.2015.56.402

Full text: PDF file (382 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2015, 56:4, 575–592

Bibliographic databases:

UDC: 517.956.8+517.956.328+517.958+535.4
Received: 10.09.2014

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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\by F.~L.~Bakharev, S.~A.~Nazarov
\paper Gaps in the spectrum of a~waveguide composed of domains with different limiting dimensions
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\vol 56
\issue 4
\pages 732--751
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\issue 4
\pages 575--592
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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. F. L. Bakharev, S. A. Nazarov, “Open waveguides in doubly periodic junctions of domains with different limit dimensions”, Siberian Math. J., 57:6 (2016), 943–956  mathnet  crossref  crossref  isi  elib
    2. G. Cardone, T. Durante, S. A. Nazarov, “The spectrum, radiation conditions and the Fredholm property for the Dirichlet Laplacian in a perforated plane with semi-infinite inclusions”, J. Differ. Equ., 263:2 (2017), 1387–1418  crossref  mathscinet  zmath  isi  scopus
    3. G. Cardone, A. Khrabustovskyi, “Spectrum of a singularly perturbed periodic thin waveguide”, J. Math. Anal. Appl., 454:2 (2017), 673–694  crossref  mathscinet  zmath  isi  scopus
    4. F. L. Bakharev, J. Taskinen, “Bands in the spectrum of a periodic elastic waveguide”, Z. Angew. Math. Phys., 68:5 (2017), 102  crossref  mathscinet  zmath  isi  scopus
    5. A.-S. Bonnet-Ben Dhia, L. Chesnel, S. A. Nazarov, “Perfect transmission invisibility for waveguides with sound hard walls”, J. Math. Pures Appl., 111 (2018), 79–105  crossref  mathscinet  zmath  isi  scopus
    6. F. L. Bakharev, M. Eugenia Perez, “Spectral gaps for the Dirichlet-Laplacian in a 3-D waveguide periodically perturbed by a family of concentrated masses”, Math. Nachr., 291:4 (2018), 556–575  crossref  mathscinet  zmath  isi  scopus
    7. T. Durante, “Dirichet Laplacian in a perforated plane with semi-infinite inclusions”, International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2017), AIP Conf. Proc., 1978, Amer. Inst. Phys., 2018, 140004-1  crossref  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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