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Time‐dependent scattering of generalized plane waves by a wedge
Author(s) -
Komech A.I.,
Merzon A.E.,
Méndez J.E. De la Paz
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3391
Subject(s) - mathematics , mathematical analysis , wedge (geometry) , neumann boundary condition , scattering , harmonic function , diffraction , plane wave , boundary value problem , uniqueness , dirichlet distribution , dirichlet boundary condition , scattering amplitude , geometry , physics , optics
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.