THE OUTGOING TIME-HARMONIC ELASTIC WAVE IN A HALF-PLANE WITH FREE BOUNDARY
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Date
2011
Journal Title
Journal ISSN
Volume Title
Publisher
SIAM PUBLICATIONS
Abstract
Under a time-harmonic assumption, we prove existence and uniqueness results for the outgoing elastic wave in an isotropic half-plane, where the source is given by a local normal stress excitation of the free boundary. This is the starting point for problems of elastic wave scattering by locally perturbed flat surfaces. The main difficulty is that the free boundary condition induces the propagation of a Rayleigh surface wave guided by the unbounded flat frontier. Due to the presence of this surface wave in the far field expansion, we need to impose a new radiation condition in order to describe both volume and surface outgoing wave behavior and to show uniqueness.
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Keywords
radiation condition, linear elasticity, half-plane, Rayleigh wave, uniqueness, INFINITE ROUGH SURFACES, RADIATION CONDITIONS, HELMHOLTZ-EQUATION, SCATTERING, UNIQUENESS