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Towards the validity of the geometrical theory of diffraction

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Function Theoretic Methods for Partial Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 561))

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References

  1. C. A. Bloom, and B. J. Matkowsky, On the validity of the geometrical theory of diffraction by convex cylinders. Arch. Rat. Mech. Anals. 33 71–90 (1969).

    Article  MathSciNet  Google Scholar 

  2. W. Franz and K. Deppermann, Theorie der Beugung am Zylinder unter Berücksichtigung der Kriechwelle, Ann der Phys. 10 361–373 (1952).

    Article  MathSciNet  MATH  Google Scholar 

  3. R. F. Goodrich and N. D. Kazarinoff, Scalar diffraction by prolate spheroids whose eccentricities are almost one. Proc. Camb. Phil. Soc. 59 167–183 (1963).

    Article  MathSciNet  MATH  Google Scholar 

  4. R. Grimshaw, High frequency scattering by finite convex regions. Comm. Pure Appl. Math. 19 167–198 (1966).

    Article  MathSciNet  MATH  Google Scholar 

  5. J. B. Keller, Diffraction by a convex cylinder. Trans. I.R.E. AP-4, 312–321 (1956).

    MathSciNet  Google Scholar 

  6. F. G. Leppington, On the short-wave asymptotic solution of a problem in acoustic radiation. Proc. Camb. Phil. Soc. 64 1131–1150 (1968).

    Article  MathSciNet  Google Scholar 

  7. B. R. Levy, Diffraction by an elliptic cylinder. J. Math. Mech. 9 147–166 (1960).

    MathSciNet  MATH  Google Scholar 

  8. R. M. Lewis, N. Bleistein and D. Ludwig, Uniform asymptotic theory of creeping waves. Comm. Pure Appl. Math. 20 295–327 (1967).

    Article  MathSciNet  MATH  Google Scholar 

  9. C. S. Morawetz and D. Ludwig, An inequality for the reduced wave operator and the justification of geometrical optics. Comm. Pure Appl. Math. 21 187–203 (1968).

    Article  MathSciNet  MATH  Google Scholar 

  10. F. W. J. Olver, Asymptotics and special functions. Academic Press, London (1974) (see also, second-order linear differential equations with two turning points. Phil. Trans. Roy. Soc. 278 137–185, (1974)).

    MATH  Google Scholar 

  11. B. D. Sleeman, Integral representations associated with high-frequency non-symmetric scattering by prolate spheroids. Quart. J. Mech. and Appl. Math. 22 405–426 (1969).

    Article  MathSciNet  MATH  Google Scholar 

  12. F. Ursell, On the short wave asymptotic theory of the wave equation (∇2+k2)φ=0. Proc. Camb. Phil Soc. 53 115–133 (1957).

    Article  MathSciNet  MATH  Google Scholar 

  13. F. Ursell, Creeping modes in a shadow. Proc. Camb. Phil. Soc. 64 171–191 (1968).

    Article  MathSciNet  Google Scholar 

  14. G. N. Watson, The diffraction of electric waves by the earth. Proc. Roy. Soc. London Ser. A 95 83–99 (1918).

    Article  MATH  Google Scholar 

  15. T. T. Wu and S. R. Seshadri, The electromagnetic theory of light II. Harvard University, Cruft Laboratory, Scientific Report No 22 (1958).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Dundee, DD1 4HN, Dundee, Scotland

    B D Sleeman

Authors
  1. B D Sleeman
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Editor information

V. Erhard Meister Wolfgang L. Wendland Norbert Weck

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© 1976 Springer-Verlag

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Sleeman, B.D. (1976). Towards the validity of the geometrical theory of diffraction. In: Meister, V.E., Wendland, W.L., Weck, N. (eds) Function Theoretic Methods for Partial Differential Equations. Lecture Notes in Mathematics, vol 561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087657

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  • DOI: https://doi.org/10.1007/BFb0087657

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08054-1

  • Online ISBN: 978-3-540-37536-4

  • eBook Packages: Springer Book Archive

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