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

Authors

  • Luis A. Cortés Vega Universidad de Antofagasta.
  • Claudio Fernández P. Universidad Católica de Chile.
  • Gustavo Perla Menzala National Laboratory of Scientific Computation; Universidade Federal de Rio de Janeiro.

DOI:

https://doi.org/10.4067/S0716-09172006000200006

Keywords:

Existence and uniqueness of outgoing solutions, linear elastic wave equation, star-shaped domain, linear velocity boundary type conditions, resonances, existencia y unicidad de soluciones externas, ecuación de onda elástica lineal.

Abstract

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.

Author Biographies

Luis A. Cortés Vega, Universidad de Antofagasta.

Facultad de Ciencias Básicas,
Departamento de Matemáticas.

Claudio Fernández, P. Universidad Católica de Chile.

Facultad de Matemáticas.

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Published

2017-05-08

How to Cite

[1]
L. A. Cortés Vega, C. Fernández, and G. Perla Menzala, “On outgoing solutions for a system of time-harmonic elastic wave in the exterior of a star-shaped domain”, Proyecciones (Antofagasta, On line), vol. 25, no. 2, pp. 205-229, May 2017.

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Artículos