[Condition de radiation et unicité pour l'onde élastique sortante dans un demi-plane avec frontière libre]
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.
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.
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@article{CRMATH_2009__347_21-22_1321_0,
author = {Mario Dur\'an and Ignacio Muga and Jean-Claude N\'ed\'elec},
title = {Radiation condition and uniqueness for the outgoing elastic wave in a half-plane with free boundary},
journal = {Comptes Rendus. Math\'ematique},
pages = {1321--1324},
publisher = {Elsevier},
volume = {347},
number = {21-22},
year = {2009},
doi = {10.1016/j.crma.2009.10.005},
language = {en},
}
TY - JOUR AU - Mario Durán AU - Ignacio Muga AU - Jean-Claude Nédélec TI - Radiation condition and uniqueness for the outgoing elastic wave in a half-plane with free boundary JO - Comptes Rendus. Mathématique PY - 2009 SP - 1321 EP - 1324 VL - 347 IS - 21-22 PB - Elsevier DO - 10.1016/j.crma.2009.10.005 LA - en ID - CRMATH_2009__347_21-22_1321_0 ER -
%0 Journal Article %A Mario Durán %A Ignacio Muga %A Jean-Claude Nédélec %T Radiation condition and uniqueness for the outgoing elastic wave in a half-plane with free boundary %J Comptes Rendus. Mathématique %D 2009 %P 1321-1324 %V 347 %N 21-22 %I Elsevier %R 10.1016/j.crma.2009.10.005 %G en %F CRMATH_2009__347_21-22_1321_0
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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