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Stationary and Time-Dependent Diffraction

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Stationary Diffraction by Wedges

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2249))

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Abstract

The time-dependent diffraction is aimed to determination of long-time asymptotics of wave processes, while the goal of stationary diffraction is the calculation of limiting amplitudes . Let us assume everywhere below in this book that the speed of light c = 1.

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References

  1. S. Agmon, Spectral properties of Schrödinger operators and scattering theory. Ann. Scuola Norm. Sup. di Pisa 4(2), 151–218 (1975)

    MATH  Google Scholar 

  2. V.M. Babich, M.A. Lyalinov, V.E. Grikurov, The Sommerfeld -Malyuzhinets Technique in Diffraction Theory (Alpha Science International, Oxford, 2007)

    Google Scholar 

  3. D.M. Eidus, The principle of limit amplitude. Russ. Math. Surv. 24(3), 24–97 (1969)

    Article  Google Scholar 

  4. A. Esquivel, A. Merzon, An explicit formula for the nonstationary diffracted wave scattered on a NN-wedge. Acta Apl. Math. 136(1), 119–145 (2015)

    Article  MathSciNet  Google Scholar 

  5. W. Ignatowsky, Reflexion elektromagnetischer Wellen an einem Drahte. Ann. der Physik 18(13), 495–522 (1905)

    Article  Google Scholar 

  6. A. Jensen, T. Kato, Spectral properties of Schrödinger operators and time-decay of the wave functions. Duke Math. J. 46, 583–611 (1979)

    Article  MathSciNet  Google Scholar 

  7. A.I. Komech, E.A. Kopylova, Dispersion Decay and Scattering Theory (Wiley, Hoboken, 2012)

    Book  Google Scholar 

  8. A.I. Komech, A.E. Merzon, Limiting amplitude principle in the scattering by wedges . Math. Methods Appl. Sci. 29(10), 1147–1185 (2006)

    Article  MathSciNet  Google Scholar 

  9. A.I. Komech, A.E. Merzon, On uniqueness and stability of Sobolev’s solution in scattering by wedges . J. Appl. Math. Phys. (ZAMP) 66(5), 2485–2498 (2015)

    Google Scholar 

  10. A.I. Komech, A.E. Merzon, J.E. De La Paz Méndez, Time-dependent scattering of generalized plane waves by wedges . Math. Methods Appl. Sci. 38(18), 4774–4785 (2015)

    Article  MathSciNet  Google Scholar 

  11. A.I. Komech, A.E. Merzon, A. Esquivel Navarrete, J.E. De La Paz Méndez, T.J. Villalba Vega, Sommerfeld’s solution as the limiting amplitude and asymptotics for narrow wedges. Math. Methods Appl. Sci., 1–14 (2018). https://doi.org/10.1002/mma.5075

    Article  Google Scholar 

  12. C. Morawetz, The limiting amplitude principle . Commun. Pure Appl. Math. 15, 349–361 (1962)

    Article  Google Scholar 

  13. S.H. Schot, Eighty years of Sommerfeld ’s radiation condition. Hist. Math. 19(4), 385–401 (1992)

    Article  MathSciNet  Google Scholar 

  14. A. Sommerfeld , Die Greensche Funktion der Schwingungsgleichung. Thematiker-Vereinigung 21, 309–353 (1912). Reprinted in Gesammelte Schriften, vol. 1, pp. 272–316

    Google Scholar 

  15. A.N. Tikhonov, A.A. Samarskii, On principle of radiation. JETP 18(2), 243–248 (1948)

    Google Scholar 

  16. B.R. Vainberg, Asymptotic Methods in Equations of Mathematical Physics (Gordon and Breach, New York, 1989)

    MATH  Google Scholar 

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Komech, A., Merzon, A. (2019). Stationary and Time-Dependent Diffraction. In: Stationary Diffraction by Wedges . Lecture Notes in Mathematics, vol 2249. Springer, Cham. https://doi.org/10.1007/978-3-030-26699-8_4

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