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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 5, Pages 793–814
DOI: https://doi.org/10.7868/S0044466914050147 (Mi zvmmf10033) 		 
This article is cited in 10 scientific papers (total in 10 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
Full-text PDF (366 kB) Citations (10)
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DOI: https://doi.org/10.7868/S0044466914050147
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.
Received: 26.06.2013
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 5, Pages 793–814
DOI: https://doi.org/10.1134/S0965542514050121
Bibliographic databases:
Document Type: Article
UDC: 519.632.4
Language: Russian
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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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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