On outgoing solutions for a system of time-harmonic elastic wave in the exterior of a star-shaped domain

• Cortés Vega, Luis A. ^[1] ; Fernández, Claudio ^[2] ; Perla Menzala, Gustavo ^[3]
  1. [1] Universidad de Antofagasta

     Universidad de Antofagasta

     Antofagasta, Chile

     
  2. [2] Pontificia Universidad Católica de Chile

     Pontificia Universidad Católica de Chile

     Santiago, Chile

     
  3. [3] Universidade Federal do Rio de Janeiro

     Universidade Federal do Rio de Janeiro

     Brasil

     

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• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 25, Nº. 2, 2006, págs. 205-229
• Idioma: inglés
• DOI: 10.4067/S0716-09172006000200006
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• Resumen

  • In this work we consider the propagation of time-harmonic elastic waves outside of a star-shaped domain with a “linear velocity at the boundary”. We describe a new approach to investigate results of existence and uniqueness for this exterior problem. To this end, we used a method similar to the one discussed in [11, 12] which has its genesis in [13] and relies on a stationary approach of resonances. The fundamental step of our approach is to reduce the unbounded nature of the problem to a bounded domain introducing an auxiliary boundary condition of Dirichlet type. In particular, we find a large region in the complex plane which is “free” of resonances.

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