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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 5, Pages 793–814 (Mi zvmmf10033)  

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

Asymptotics of eigenvalues of the Dirichlet problem in a skewed $\mathcal{T}$-shaped waveguide

S. A. Nazarov

St. Petersburg State University, Universitetskii pr. 28, Staryi Peterhof, St. Petersburg, 198504, Russia

Abstract: Asymptotics are constructed and justified for the eigenvalues of the Dirichlet problem for the Laplacian in a waveguide consisting of a unit strip and a semi-infinite strip joined at a small angle $\varepsilon\in(0,\pi/2)$. Some properties of the discrete spectrum are established, and open questions are stated.

Key words: $\mathcal{T}$-shaped waveguide, Dirichlet problem for the Laplacian, discrete spectrum, asymptotics, boundary layer.

DOI: https://doi.org/10.7868/S0044466914050147

Full text: PDF file (366 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:5, 793–814

Bibliographic databases:

UDC: 519.632.4
Received: 26.06.2013

Citation: S. A. Nazarov, “Asymptotics of eigenvalues of the Dirichlet problem in a skewed $\mathcal{T}$-shaped waveguide”, Zh. Vychisl. Mat. Mat. Fiz., 54:5 (2014), 793–814; Comput. Math. Math. Phys., 54:5 (2014), 793–814

Citation in format AMSBIB
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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, “Bounded solutions in a $\mathrm{T}$-shaped waveguide and the spectral properties of the Dirichlet ladder”, Comput. Math. Math. Phys., 54:8 (2014), 1261–1279  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. S. A. Nazarov, “Localization of longitudinal and transverse oscillations in a thin curved elastic gasket”, Dokl. Phys., 60:10 (2015), 446–450  crossref  mathscinet  isi  elib  scopus
    3. F. L. Bakharev, S. G. Matveenko, S. A. Nazarov, “Discrete spectrum of x-shaped waveguide”, St. Petersburg Math. J., 28:2 (2017), 171–180  mathnet  crossref  mathscinet  isi  elib
    4. S. A. Nazarov, “Discrete spectrum of cranked quantum and elastic waveguides”, Comput. Math. Math. Phys., 56:5 (2016), 864–880  mathnet  crossref  crossref  isi  elib
    5. S. A. Nazarov, “Open waveguides in a thin Dirichlet ladder: I. Asymptotic structure of the spectrum”, Comput. Math. Math. Phys., 57:1 (2017), 156–174  mathnet  crossref  crossref  isi  elib
    6. M. Khalile, K. Pankrashkin, “Eigenvalues of Robin Laplacians in infinite sectors”, Math. Nachr., 291:5-6 (2018), 928–965  crossref  mathscinet  zmath  isi  scopus
    7. S. A. Nazarov, “Asymptotics of the deflection of a cruciform junction of two narrow Kirchhoff plates”, Comput. Math. Math. Phys., 58:7 (2018), 1150–1171  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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