Short-wavelength diffraction by a contours with non-smooth curvature. Boundary layer approach

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.