Comptes Rendus
Mathematical Problems in Mechanics
Radiation condition and uniqueness for the outgoing elastic wave in a half-plane with free boundary
Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1321-1324.

In this Note we deduce an explicit Sommerfeld-type radiation condition which is convenient to prove the 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.

Dans cette Note, nous exhibons une condition de radiation explicite, du type Sommerfeld, qui nous permet de montrer (dans le domaine fréquenciel) l'unicité des solutions du problème d'onde élastique sortante dans un demi-plan avec frontière libre. Cette expression est obtenue par une analyse asymptotique rigoureuse de la fonction de Green's associée. La difficulté principale est que la condition de bord de frontière libre permet la propagation d'une onde de Rayleigh qui n'est pas négligeable dans le champ lointain. Nous donnons également un résultat d'existence pour ce problème.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.10.005

Mario Durán 1; Ignacio Muga 2; Jean-Claude Nédélec 3

1 Facultad de Ingeniería, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile
2 Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso, Chile
3 CMAP, École polytechnique, 91128 Palaiseau cedex, France
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     title = {Radiation condition and uniqueness for the outgoing elastic wave in a half-plane with free boundary},
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Mario Durán; Ignacio Muga; Jean-Claude Nédélec. Radiation condition and uniqueness for the outgoing elastic wave in a half-plane with free boundary. Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1321-1324. doi : 10.1016/j.crma.2009.10.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.10.005/

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[3] Mario Durán; Ignacio Muga; Jean-Claude Nédélec The Helmholtz equation in a locally perturbed half-plane with passive boundary, IMA J. Appl. Math., Volume 71 (2006) no. 6, pp. 853-876

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