Abstract
The spectrum of the Dirichlet problem for the Laplace operator in a plane T-shaped waveguide is investigated. The critical width of the half-strip branch is determined such that, if the width is greater, the waveguide has no discrete spectrum. The existence of a critical width is proved theoretically.
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Dedicated to Academician A.A. Dorodnicyn on the Occasion of the Centenary of His Birth
Original Russian Text © S.A. Nazarov, A.V. Shanin, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 1, pp. 104–119.
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Nazarov, S.A., Shanin, A.V. Calculation of characteristics of trapped modes in T-shaped waveguides. Comput. Math. and Math. Phys. 51, 96–110 (2011). https://doi.org/10.1134/S0965542511010118
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DOI: https://doi.org/10.1134/S0965542511010118