×

Rigorous justification of the shortwave asymptotic theory of diffraction in the shadow zone. (English) Zbl 0375.35017


MSC:

35J10 Schrödinger operator, Schrödinger equation
35B99 Qualitative properties of solutions to partial differential equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] V. S. Buslaev, ?Potential theory and geometrical optics,? J. Sov. Math.,2, No. 2, 204?209 (1974). · Zbl 0284.35017
[2] J. B. Keller, ?Diffraction by a convex cylinder,? Trans. IRE Antennas and Propagation,AP-4, 312?321 (1956).
[3] V. A. Fok, Electromagnetic Wave Diffraction and Propagation Problems [in Russian], Izd. Sovet-skoe Radio, Moscow (1970).
[4] V. M. Babich and V. S. Buldyrev, Asymptotic Methods in Shortwave Diffraction Problems [in Russian], Izd. Nauka (1972). · Zbl 0255.35002
[5] R. M. Lewis, N. Bleistein, and D. Ludwig, ?Uniform asymptotic theory of creeping waves,? Commun. Pure Appl. Math.,20, No. 2, 295?327 (1967). · Zbl 0154.12103
[6] W. Franz and K. Deppermann, ?Theorie der Beugung am Zylinder unter Berücksichtigung der Kriechwelle,? Ann. Phys.,10, 361?373 (1952). · Zbl 0047.20201
[7] C. O. Bloom, ?Diffraction by a hyperbolic cylinder,? Bull. Amer. Math. Soc.,74, No. 3 (1968).
[8] F. Ursell, ?Creeping modes in a shadow,? Proc. Cambridge Phil. Soc.,64, No. 1, 171?191 (1968).
[9] C. O. Bloom and B. J. Matkowsky, ?On the validity of the geometrical theory of diffraction by a convex cylinder,? Arch. Rational Anal. Mech.,33, No. 1, 71?90 (1969).
[10] V. M. Babich and I. V. Olimpiev, ?Estimation of the field in the shadow zone in the diffraction of a cylindrical wave by a bounded convex cylinder,? in: Proc. Third All-Union Sympos. Wave Diffraction [in Russian], Izd. Nauka (1964). · Zbl 0137.07604
[11] F. Ursell, ?On the shortwave asymptotic theory of the wave equation (?2+?2)?=o,? Proc. Cambridge Phil. Soc.,53, 115?133 (1957).
[12] V. S. Buslaev, ?Shortwave asymptotic theory of diffraction by smooth convex contours,? Trudy Matem. Inst.,23, No. 2, 14?117 (1964).
[13] V. M. Babich, ?Shortwave asymptotic behavior of the Green function for the Helmholtz equation,? Matem. Sborn.,65, No. 4, 577?630 (1964).
[14] I. A. Molotkov, ?Field of a point source situated outside a convex curve,? in: Problems of Mathematical Physics [in Russian], No. 4, Izd. LGU (1970), pp. 83?111.
[15] A. Erdélyi and M. Wyman, ?The asymptotic evaluation of certain integrals,? Arch. Rational Appl. Mech.,14, No. 3, 217?260 (1963). · Zbl 0168.37903
[16] R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 2: Partial Differential Equations, Wiley, New York (1962). · Zbl 0099.29504
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.