International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 64, Pages 3485-3498

A note on resonant frequencies for a system of elastic wave equations

Luis A. Cortés-Vega

Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Casilla 170, Antofagasta, Chile

Received 26 March 2003

Copyright © 2004 Luis A. Cortés-Vega. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a rather simple proof of the existence of resonant frequencies for the direct scattering problem associated to a system of elastic wave equations with Dirichlet boundary condition. Our approach follows techniques similar to those in Cortés-Vega (2003). The proposed technique relies on a stationary approach of resonant frequencies, that is, the poles of the analytic continuation of the solution.