Abstract
The Helmholtz equation in a closed domain that is an equilateral triangle with inhomogeneous impedance boundary conditions is considered. A functional equation in which the unknown function is the Fourier-image of a wave field on the boundary of the domain is constructed. This functional equation is solved for the case of homogeneous boundary conditions (the problem on eigenvalues), as well as for the case of inhomogeneous boundary conditions in the absence of the resonance. Bibliography: 4 titles.
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References
G. Lamé,Lecons sur la Theorie Mathématique de l'Elasticité des Corps Solides, Bachelier, Paris (1852).
G. D. Malyuzhenetz, “Excitation, reflection, and radiation of surface waves in a wedge with known impedances of the boundary”,Dokl. Akad. Nauk SSSR,121, No. 3, 436–439 (1958).
I. M. Ryzhik and I.S. Gradstein,Tables of Integrals, Sums, and Products [in Russian], Leningrad (1951).
A. V. Shanin, “On wave excitation in a wedge-shaped region”,Acoustic Phys.,42, No. 5, 696–701 (1996).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 300–318.
Translated by A. V. Shanin.
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Shanin, A.V. Excitation of a wave field in a triangular domain with impedance boundary conditions. J Math Sci 102, 4328–4338 (2000). https://doi.org/10.1007/BF02673863
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DOI: https://doi.org/10.1007/BF02673863