Diffraction by a line of jump of curvature (a special case)

We consider the diffraction of shortwave radiation by a convex body with the boundary having a jump of curvature. In cross-section the boundary consists of two parts: convex and planar, smoothly joined. A special case of diffraction by the curve with the curvature jump is under consideration: the jump point is situated in the penumbra region. Using asymptotic methods we obtain new formulae for the wave field in the main approximation in problems with Dirichlet, Neumann and impedance boundary conditions.