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Green’s Function for the Helmholtz Equation in a Polygonal Domain of Special Form with Ideal Boundary Conditions

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A formal approach for the construction of the Green’s function in a polygonal domain with the Dirichlet boundary conditions is proposed. The complex form of the Kontorovich–Lebedev transform and the reduction to a system of integral equations is employed. The far-field asymptotics of the wave field is discussed.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    M. A. Lyalinov

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  1. M. A. Lyalinov
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Correspondence to M. A. Lyalinov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 471, 2018, pp. 150–167.

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Lyalinov, M.A. Green’s Function for the Helmholtz Equation in a Polygonal Domain of Special Form with Ideal Boundary Conditions. J Math Sci 243, 734–745 (2019). https://doi.org/10.1007/s10958-019-04575-5

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  • DOI: https://doi.org/10.1007/s10958-019-04575-5

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