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Short-Wavelength Diffraction by a Contour with Nonsmooth Curvature. Boundary Layer Approach

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We consider the short-wave length diffraction by a contour with a nonsmooth curvature, whose jth derivative (j = 1, 2, . . .) has a discontinuity at a point. The asymptotic formulas describing the effect of curvature’s nonsmoothness on the wavefield are constructed in the framework of the rigorous boundary layer method. An expression for a cylindrical diffracted wave is derived. A description of the wavefield in a vicinity of the limit ray at a small distance from the contour is given in terms of the parabolic cylinder functions.

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Authors and Affiliations

  1. St. Petersburg Department of Steklov Institute of Mathematics, St. Petersburg State University, St. Petersburg, Russia

    E. A. Zlobina

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  1. E. A. Zlobina
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Correspondence to E. A. Zlobina.

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Dedicated to V. M. Babich’s 90th anniversary

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 493, 2020, pp. 169–185.

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Zlobina, E.A. Short-Wavelength Diffraction by a Contour with Nonsmooth Curvature. Boundary Layer Approach. J Math Sci 277, 586–597 (2023). https://doi.org/10.1007/s10958-023-06865-5

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