Journal of Mathematical Sciences

, Volume 73, Issue 3, pp 330–341 | Cite as

Elastic wave diffraction by a wedge-shaped inclusion

  • B. V. Budaev
Article
  • 25 Downloads

Abstract

By means of Sommerfeld integrals techniques the problem of diffraction is reduced to a functional equation in a complex domain. Such an equation is known in the literature as an equation with non-Carleman translation. The theory of pseudodifferential operators reduces to the theory of functional equations and, consequently, the problem of diffraction, to a Fredholm integral equation. Bibliography: 12 titles.

Keywords

Integral Equation Functional Equation Elastic Wave Pseudodifferential Operator Complex Domain 

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Literature Cited

  1. 1.
    B. V. Budaev, “Diffraction of elastic waves by a wedge. General approach,” (Preprint), LOMI, No. E-13-86, Leningrad (1988).Google Scholar
  2. 2.
    B. V. Budaev, “Diffraction of elastic waves by a wedge. II,” (Preprint), LOMI, No. E-6-89, Leningrad (1990).Google Scholar
  3. 3.
    B. V. Budaev, “Diffraction of elastic waves by a stress free wedge. Reduction to a singular integral equation,”Zap. Nauchn. Sem. Leningrad. Otd. Mat. Inst. Steklov (LOMI),179, Leningrad, 37–45 (1989).MATHGoogle Scholar
  4. 4.
    B. V. Budaev, “Eigenfunctions of a stress-free elastic wedge,” in:Problems in the Dynamic Theory of Seismic Wave Propagation [in Russian], vol. 29, Leningrad (1989), pp. 36–40.Google Scholar
  5. 5.
    S. N. Karp and F. G. Karal, “The elastic field behavior in the neighborhood of a crack of arbitrary angle,”Comm. Pure Appl. Math.,15, No. 4, 413–421 (1962).MathSciNetGoogle Scholar
  6. 6.
    G. D. Malyuzhinets,The Sommerfeld Integrals and Their Applications in Diffraction Theory [in Russian], NPO “Rumb,” Leningrad (1979).Google Scholar
  7. 7.
    G. D. Malyuzhinets, “Sound's radiation by oscilating faces of an arbitrary wedge,”Akust. Zh.,1, No 2, 144–164 (1955).Google Scholar
  8. 8.
    G. D. Malyuzhinets, “Connection between Sommerfeld integrals and Kantorovich-Lebedev transform,”Dokl. Akad. Nauk SSSR,119, No 1, 49–51 (1958).MATHMathSciNetGoogle Scholar
  9. 9.
    M. S. Bobrovnikov and V. V. Fisanov,Diffraction in Wedge-shaped Regions [in Russian], Tomsk University, Tomsk (1988).Google Scholar
  10. 10.
    M. A. Shubin,Pseudodifferential Operators and Spectral Theory [in Russian], Nauka, Moscow (1978).Google Scholar
  11. 11.
    F. Treves,Introduction to Pseudodifferential and Fourier Operators, Vol. 2, Pseudodifferential Operators, Plenum Press, New York-London (1982).Google Scholar
  12. 12.
    L. Hermander,The Analysis of Linear Partial Differential Operators III. Pseudodifferential Operators, Springer-Verlag, New York (1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • B. V. Budaev

There are no affiliations available

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