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Babich, V. M.; Grigor’eva, N. S.

Shortwave diffraction by an oblate spheroid. (English) Zbl 0396.35007

J. Sov. Math. 9, 412-453 (1978).
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scan of Zbl 0396.35007

MSC:

35B99 Qualitative properties of solutions to partial differential equations
35J10 Schrödinger operator, Schrödinger equation

Keywords:

Watson’s Method; Neumann Problem for the Helmholtz Equation; Oblate Spheroid; Diffractin of Shortwaves; Zone of Deep Shadow

Citations:

Zbl 0363.35008
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Full Text: DOI

References:

[1] B. R. Levy and J. B. Keller, ”Diffraction by a spheroid,” Canad. J. Phys.,38, No. 1, 128–144 (1960). · Zbl 0092.20603 · doi:10.1139/p60-012
[2] R. E. Goodrich and N. D. Kozarinoff, ”Scalar diffraction by prolate spheroids whose eccentricities are almost one,” Proc. Cambr. Phil. Soc.,59, No. 1, 167–183 (1963). · Zbl 0118.43604 · doi:10.1017/S0305004100002127
[3] B. D. Sleeman, ”Integral representations associated with high-frequency nonsymmetric scattering by prolate spheroids,” Quart. J. Mech. Appl. Math.,22, No. 4, 405–426 (1969). · Zbl 0185.18701 · doi:10.1093/qjmam/22.4.405
[4] B. D. Sleeman, ”Diffraction at short wavelengths by a prolate spheroid,” J. Inst. Math. Applic.,5, No. 4, 432–442 (1969). · Zbl 0189.10203 · doi:10.1093/imamat/5.4.432
[5] T. F. Pankratova, ”On the eigenfunctions of the Laplace operator on the surface of a triaxial ellipsoid and in the region exterior to it,” Zap. Nauch. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,9, 192–211 (1968). · Zbl 0195.38901
[6] F. G. Leppington, ”Creeping waves in the shadow of an elliptic cylinder,” J. Inst. Math. Applic.,3, No. 4, 388–402 (1967). · Zbl 0153.56503 · doi:10.1093/imamat/3.4.388
[7] V. M. Babich, ”On the shortwave asymptotic behavior of Green’s functions for the Helmholtz equation,” Mat. Sb.,65 (107), No. 4, 576–630 (1964).
[8] V. M. Babich and N. S. Grigor’eva, ”Uniform asymptotic expansions of functions related to an oblate spheroid,” Collection of Articles on Mathematical Questions in the Theory of Wave Propagation, Zap. Nauch. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,34, 6–23 (1973).
[9] V. M. Babich, ”Finding the saddle point in the case of the problem of an ellipse,” Zap. Nauch. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,17, 20–24 (1970).
[10] D. Ludwig, ”Uniform asymptotic expansion of the field scattered by a convex object at high frequencies,” Comm. Pure Appl. Math.,20, No. 1, 103–138 (1967). · Zbl 0154.12802 · doi:10.1002/cpa.3160200103
[11] R. M. Lewis, N. Bleistein, and D. Ludwig, ”Uniform asymptotic theory of creeping waves,” Comm. Pure Appl. Math.,20, No. 2, 295–328 (1967). · Zbl 0154.12103 · doi:10.1002/cpa.3160200205
[12] C. Chester, B. Friedman, and F. Ursell, ”An extension of the method of steepest descent,” Proc. Cambridge Philos. Soc.,53, No. 3, 599–611 (1957). · Zbl 0082.28601 · doi:10.1017/S0305004100032655
[13] M. F. Fedoryuk, ”The method of stationary phase for multidimensional integrals,” Zh. Vychisl. Mat. Mat. Fiz.,2, No. 1, 145–150 (1962). · Zbl 0122.12401
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