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Title: Elastic scattering from rough surfaces in three dimensions
Consider the elastic scattering of a plane or point incident wave by an unbounded and rigid rough surface. The angular spectrum representation (ASR) for the time-harmonic Navier equation is derived in three dimensions. The ASR is utilized as a radiation condition to the elastic rough surface scattering problem. The uniqueness is proved through a Rellich-type identity for surfaces given by uniformly Lipschitz functions. In the case of flat surfaces with local perturbations, an equivalent variational formulation is deduced in a truncated bounded domain and the existence of solutions are shown for general incoming waves. The main ingredient of the proof is the radiating behavior of the Green tensor to the first boundary value problem of the Navier equation in a half-space.  more » « less
Award ID(s):
1912704
PAR ID:
10182368
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Journal of differential equations
Volume:
269
ISSN:
0022-0396
Page Range / eLocation ID:
4045-4078
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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