Radiation condition and uniqueness for the outgoing elastic wave in a half-plane with free boundary. http://dx.doi.org/10.1016/j.crma.2009.10.005

Abstract

In this note we deduce an explicit Sommerfeld-type radiation condition which is convenient to prove teh uniqueness for the time-harmonic outgoing wave problem in an isotropic elastic half-plane with free boundary condition. The expression is obtained from a rigorous asymptotic analysis of the associated Green’s function. The main difficulty is that the free boundary condition allows the propagation of a Rayleigh wave which cannot be neglected in the far field expansion. We also give the existence result for this problem.