AN EXAMPLE OF SURFACE ELASTIC-WAVES ARISING FROM THE INTERIOR

In this paper we shall study singularities to solutions of elastic wave equations which propagate on the boundary. Typical surface waves of elastic wave equations in isotropic media are Rayleigh waves. However, it is easy to show that if the support of the initial data of a solution is contained in the interior, the solution does not have singularities corresponding to Rayleigh waves. The purpose of this paper is to show that there exist a different kind of surface waves arising from the interior, which are P gliding rays. Our surface singularities are derived from a limited phenomenon of a reflection of elastic waves, which is quiet different from a reflection of usual waves.