Volume 18, Number 2, April-June 2012
|Page(s)||427 - 451|
|Published online||22 June 2011|
Spectral analysis in a thin domain with periodically oscillating characteristics
I.C.T.I. - Carnegie Mellon | Portugal, F.C.T./C.M.A. da U.N.L.,
Quinta da Torre, 2829–516
2 Departamento de Matemática da F.C.T./C.M.A. da U.N.L., Quinta da Torre, 2829–516 Caparica, Portugal
3 Narvik University College, P.O. Box 385, 8505 Narvik, Norway
4 P.N. Lebedev Physical Institute RAS, Leninski prospect 53, Moscow 119991, Russia
The paper deals with a Dirichlet spectral problem for an elliptic operator with ε-periodic coefficients in a 3D bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is much less than δ(δ = ετ, τ < 1), or ε is much greater than δ(δ = ετ, τ > 1). We consider all three cases.
Mathematics Subject Classification: 35P20 / 49R05 / 47A75 / 35B27 / 81Q10
Key words: Spectral analysis / dimension reduction / periodic homogenization / Γ-convergence / asymptotic expansions
© EDP Sciences, SMAI, 2011
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