Diffraction of creeping waves from a point of curvature jump on the boundary of a domain (The point of transition of the convex boundary into the concave boundary)

Abstract

The problem of diffraction of a creeping wave propagating in a domain near the convex part of the boundary and overrunning a point where the convex boundary transforms to the concave one is studied. The tangent to the boundary is continuous at this point, but the derivative of the tangent has the jump. The Green's function to the right of the point of jump of curvature is a superposition of whispering gallery waves. The Dirichlet, Neumann, and impedance boundary conditions are considered. The formulas for the boundary current and for the diffraction coefficients related to the problem are obtained. Bibliography: 3 titles.