Geodesic
Short-wavelength diffraction by a contours with non-smooth curvature. Boundary layer approach
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 50, Tome 493 (2020), pp. 169-185

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We consider the short-wavelength diffraction by a contour with non-smooth curvature, whose $j$-th derivative ($j=1, 2, \ldots$) has a discontinuity at a point. Asymptotic formulas describing the effect of non-smoothness of curvature on the wavefield are constructed in a framework of rigorous boundary layer method. Аn expression for cylindrical diffracted wave is derived. The wavefield in the vicinity of the limit ray at small distances from the contour is described in terms of the parabolic cylinder functions. 
@article{ZNSL_2020_493_a11,
     author = {E. A. Zlobina},
     title = {Short-wavelength diffraction by a contours with non-smooth curvature. {Boundary} layer approach},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {169--185},
     publisher = {mathdoc},
     volume = {493},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a11/}
}
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E. A. Zlobina. Short-wavelength diffraction by a contours with non-smooth curvature. Boundary layer approach. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 50, Tome 493 (2020), pp. 169-185. http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a11/