Time‐dependent scattering of generalized plane waves by a wedge |
| |
| Authors: | A.I. Komech A.E. Merzon J.E. De la Paz Méndez |
| |
| Affiliation: | 1. Faculty of Mathematics, University of Vienna, Vienna, Austria;2. Institute for the Information Transmission Problems of RAS, Moscow, Russia;3. Institute of Physics and Mathematics, University of Michoacán of San Nicolas de Hidalgo, Morelia, Michoacán, México |
| |
| Abstract: | We obtain explicit formulas for the scattering of plane waves with arbitrary profile by a wedge under Dirichlet, Neumann and Dirichlet‐Neumann boundary conditions. The diffracted wave is given by a convolution of the profile function with a suitable kernel corresponding to the boundary conditions. We prove the existence and uniqueness of solutions in appropriate classes of distributions and establish the Sommerfeld type representation for the diffracted wave. As an application, we establish (i) stability of long‐time asymptotic local perturbations of the profile functions and (ii) the limiting amplitude principle in the case of a harmonic incident wave. Copyright © 2015 John Wiley & Sons, Ltd. |
| |
| Keywords: | scattering plane wave subclass35Q60 78A45 35C15 |
|
|
