Mathematical Problems in Mechanics
Waves in a thin and periodically oscillating medium
Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 579-584.

We study the asymptotic behavior of the spectrum of an elliptic operator with periodically oscillating coefficients, in a thin domain, with vanishing Dirichlet conditions. Two cases are treated: the case where the periodicity of the oscillations and the thickness of the domain have the same order of magnitude and the case where the oscillations have a frequency much greater than the thickness of the domain. A physical motivation can be to understand the behavior of the probability density associated to the wave function of a particle confined to a very thin domain, with periodically varying characteristics.

On étudie le comportement asymptotique du spectre d'un problème elliptique à coefficients périodiques dans un domaine mince, à condition de Dirichlet nulle. On analyse deux cas : le cas où la périodicité des oscillations est du même ordre que l'épaisseur du domaine et le cas où la fréquence des oscillations est trés grande devant l'épaisseur. Une motivation physique est de comprendre le comportement de la densité de probabilité associée à la fonction d'onde d'une particule dans un domaine mince dont les propriétés oscillent fortement.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.03.007
Ferreira, Rita 1; Mascarenhas, M. Luísa 2

1 C.M.A.-U.N.L., Quinta da Torre, 2829-516 Caparica, Portugal
2 Departamento de Matemática da F.C.T.-U.N.L. e C.M.A.-U.N.L., Quinta da Torre, 2829-516 Caparica, Portugal
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Ferreira, Rita; Mascarenhas, M. Luísa. Waves in a thin and periodically oscillating medium. Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 579-584. doi : 10.1016/j.crma.2008.03.007. http://www.numdam.org/articles/10.1016/j.crma.2008.03.007/

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