Abstract
In the paper an asymptotic expansion (as κ→∞, κ the wave number) is proved for the Green function of the problem of diffraction by a smooth convex body in two cases: when one of the points of the source or observer lies on the boundary while the other is an arbitrary distance from the boundary and also when both points lie off the boundary but not far from it. The two-dimensional Dirichlet problem is considered.
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Literature cited
V. B. Filippov, “On the rigorous justification of the short-wave asymptotics for the diffraction problem in the shadow zone,” J. Sov. Math.,6, No. 5 (1976).
A. B. Zayaev and V. B. Filippov, “On rigorous justification of asymptotic solutions of ‘creeping-wave’ type,” J. Sov. Math.,30, No. 5 (1985).
V. M. Babich and V. S. Buldyrev, Asymptotic Methods in Problems of the Diffraction of Short Waves [in Russian], Moscow (1972).
V. M. Babich and N. Ya. Kirpichnikova, The Method of the Boundary Layer in Diffraction Problems [in Russian], Leningrad (1974).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 140, pp. 49–60, 1984.
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Zayaev, A.B., Filippov, V.B. Rigorous justification of the Friedlander-Keller formulas. J Math Sci 32, 134–143 (1986). https://doi.org/10.1007/BF01084150
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DOI: https://doi.org/10.1007/BF01084150