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The Field of a Point Source Located Outside a Convex Curve

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Part of the book series: Topics in Mathematical Physics ((TOMP,volume 4))

Abstract

The present paper is devoted to constructing the high-frequency asymptotics of the solution of the problem in the plane of a point source located on the side of a curvilinear boundary S where the shadow zone appears.

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Literature Cited

  1. V. S. Buslaev, “On formulas of shortwave asymptotics in the problem of diffraction by convex bodies,” Vestn. Leningr. Gos. Univ., No. 13 (1962).

    Google Scholar 

  2. G. D. Malyuzhinets and L. A. Vainshtein, “Transverse diffusion in diffraction by an impedance cylinder of large radius,” Radiotekhn. i Elektronika, Vol. 6, No. 8, No. 9 (1961).

    Google Scholar 

  3. V. A. Fok and L. A. Vainshtein, “Transverse diffusion in diffraction by a convex cylinder with smoothly varying curvature,” Radiotekhn. i Elektronika, Vol. 8, No. 3 (1963).

    Google Scholar 

  4. I. A. Molotkov, “Diffraction by a convex contour with smoothly varying radius of curvature and impedance,” in Topics in Mathematical Physics, Vol. 2, Consultants Bureau, New York (1968).

    Google Scholar 

  5. V. M. Babich, “Estimate of the Green’s function for the Helmholtz equation in the shadow zone,” Vestn. Leningr. Gos. Univ., No. 7 (1965).

    Google Scholar 

  6. V. M. Babich and I. V. Olimpiev, “Estimate of the field in the shadow zone for diffraction of a cylindrical wave by a bounded convex cylinder,” The Third All-Union Symposium on the Diffraction of Waves, Nauka, Moscow (1964).

    Google Scholar 

  7. F. Friedlander, Sound Pulses, Cambridge (1958).

    MATH  Google Scholar 

  8. V. A. Fok, Tables of Airy Functions, Leningrad (1946).

    Google Scholar 

  9. G. I. Petrashen’, N. S. Smirnova, and G. I. Makarov, “On asymptotic representations of cylinder functions,” Uch. Zap. Leningr. Gos. Univ., No. 170 (1953).

    Google Scholar 

  10. F. Ursell, “On the shortwave asymptotic theory of the wave equation (Δ2 + k2)φ = 0,” Proc. Cambridge Phil. Soc, Vol. 53, No. 1 (1957).

    Google Scholar 

  11. V. S. Buldyrev, “Wave propagation near a curved surface of an inhomogeneous body,” in: Topics in Mathematical Physics, Vol. 2, Consultants Bureau, New York (1968).

    Google Scholar 

  12. V. S. Buldyrev, “Interference of shortwaves in the problem of diffraction by a nonhomo-geneous cylinder of arbitrary cross section,” Izv. Vuzov, Radiofizika, Vol. 10, No. 5 (1967).

    Google Scholar 

  13. M. A. Leontovich and V. A. Fok, “Solution of the problem of propagation of electromagnetic waves along the surface of the earth by the method of the parabolic equation,” in: Investigation of the Propagation of Radio Waves, Vol. 2, Izd. Akad. Nauk SSSR, Moscow (1948).

    Google Scholar 

  14. I. A. Molotkov, “The Green’s function for the problem of diffraction by a convex cylinder with variable impedance,” Tr. Matern. Inst. im V. A. Steklova Dokl. Akad. Nauk SSSR (MIAN), Vol. 95 (1968).

    Google Scholar 

  15. I. A. Molotkov, “Diffraction by a smooth convex cylinder with two propagation speeds,” Vestn. Leningr. Gos. Univ., No. 10, pp. 69–79 (1967).

    Google Scholar 

  16. V. M. Babich, “On the analytic continuation of the resolvent of the exterior problem for the Laplace operator to the second sheet,” in: The Theory of Functions, Functional Analysis, and Their Applications, Vol. 3, Izd. Khar’kovsk. Gos. Univ. (1966).

    Google Scholar 

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© 1971 Consultants Bureau, New York

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Molotkov, I.A. (1971). The Field of a Point Source Located Outside a Convex Curve. In: Birman, M.S. (eds) Spectral Theory and Wave Processes. Topics in Mathematical Physics, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-8926-2_8

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  • DOI: https://doi.org/10.1007/978-1-4684-8926-2_8

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-8928-6

  • Online ISBN: 978-1-4684-8926-2

  • eBook Packages: Springer Book Archive

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