# Spectral analysis in a thin domain with periodically oscillating characteristics

Rita Ferreira; Luísa M. Mascarenhas; Andrey Piatnitski

ESAIM: Control, Optimisation and Calculus of Variations (2012)

- Volume: 18, Issue: 2, page 427-451
- ISSN: 1292-8119

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topFerreira, Rita, Mascarenhas, Luísa M., and Piatnitski, Andrey. "Spectral analysis in a thin domain with periodically oscillating characteristics." ESAIM: Control, Optimisation and Calculus of Variations 18.2 (2012): 427-451. <http://eudml.org/doc/272885>.

@article{Ferreira2012,

abstract = {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.},

author = {Ferreira, Rita, Mascarenhas, Luísa M., Piatnitski, Andrey},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {spectral analysis; dimension reduction; periodic homogenization; Γ-convergence; asymptotic expansions; -convergence},

language = {eng},

number = {2},

pages = {427-451},

publisher = {EDP-Sciences},

title = {Spectral analysis in a thin domain with periodically oscillating characteristics},

url = {http://eudml.org/doc/272885},

volume = {18},

year = {2012},

}

TY - JOUR

AU - Ferreira, Rita

AU - Mascarenhas, Luísa M.

AU - Piatnitski, Andrey

TI - Spectral analysis in a thin domain with periodically oscillating characteristics

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2012

PB - EDP-Sciences

VL - 18

IS - 2

SP - 427

EP - 451

AB - 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.

LA - eng

KW - spectral analysis; dimension reduction; periodic homogenization; Γ-convergence; asymptotic expansions; -convergence

UR - http://eudml.org/doc/272885

ER -

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