TY - JOUR
T1 - Waves in a thin and periodically oscillating medium
AU - Ferreira, Rita
AU - Mascarenhas, M. Luísa
N1 - Funding Information:
This research was supported by POCI/MAT/60587/2004, by FCT-Plurianual (CMA) and by SFRH/BD/25573/2005. The authors thank M. Bendsœ for suggesting the problem, D. Krejcˇirík and D. Borisov for having pointed out some references, and CMAF for the hospitality.
PY - 2008/5
Y1 - 2008/5
N2 - 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. To cite this article: R. Ferreira, M.L. Mascarenhas, C. R. Acad. Sci. Paris, Ser. I 346 (2008).
AB - 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. To cite this article: R. Ferreira, M.L. Mascarenhas, C. R. Acad. Sci. Paris, Ser. I 346 (2008).
UR - http://www.scopus.com/inward/record.url?scp=43049088408&partnerID=8YFLogxK
U2 - 10.1016/j.crma.2008.03.007
DO - 10.1016/j.crma.2008.03.007
M3 - Article
AN - SCOPUS:43049088408
SN - 1631-073X
VL - 346
SP - 579
EP - 584
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 9-10
ER -