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Diffraction and Weber functions. (English) Zbl 0889.35023
Summary: The diffraction of harmonic plane waves at a perfectly conducting half-plane leads to a Dirichlet or Neumann problem for the two-dimensional (2D) Helmholtz equation. As proved by Bateman the solution may be expressed in terms of Weber functions. We first prove that his result can be generalized to a perfectly conducting wedge. Then, assuming that the electromagnetic properties of a diffracting obstacle can be described by a surface impedance, we analyze the diffraction at nonperfectly conducting planes and wedges; this corresponds to a mixed boundary value problem for the 2D Helmholtz equation.
MSC:
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
78A40Waves and radiation (optics)
35L20Second order hyperbolic equations, boundary value problems
76D33Waves in incompressible viscous fluids