Spectral analysis in a thin domain with periodically oscillating characteristics

Rita Ferreira; Luísa M. Mascarenhas; Andrey Piatnitski

doi:10.1051/cocv/2011100

Spectral analysis in a thin domain with periodically oscillating characteristics

Rita Ferreira^*, Luísa M. Mascarenhas, Andrey Piatnitski

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 = ε ^τ, τ < 1), or ε is much greater than δ(δ = ε ^τ, τ > 1). We consider all three cases.

Original language	English (US)
Pages (from-to)	427-451
Number of pages	25
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	18
Issue number	2
DOIs	https://doi.org/10.1051/cocv/2011100
State	Published - Apr 2012
Externally published	Yes

Keywords

Asymptotic expansions
Dimension reduction
Periodic homogenization
Spectral analysis
Γ-convergence

ASJC Scopus subject areas

Control and Systems Engineering
Control and Optimization
Computational Mathematics

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10.1051/cocv/2011100

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

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 = ε τ, τ < 1), or ε is much greater than δ(δ = ε τ, τ > 1). We consider all three cases.",

keywords = "Asymptotic expansions, Dimension reduction, Periodic homogenization, Spectral analysis, Γ-convergence",

author = "Rita Ferreira and Mascarenhas, {Lu{\'i}sa M.} and Andrey Piatnitski",

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T1 - Spectral analysis in a thin domain with periodically oscillating characteristics

AU - Ferreira, Rita

AU - Mascarenhas, Luísa M.

AU - Piatnitski, Andrey

PY - 2012/4

Y1 - 2012/4

N2 - 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 = ε τ, τ < 1), or ε is much greater than δ(δ = ε τ, τ > 1). We consider all three cases.

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 = ε τ, τ < 1), or ε is much greater than δ(δ = ε τ, τ > 1). We consider all three cases.

KW - Asymptotic expansions

KW - Dimension reduction

KW - Periodic homogenization

KW - Spectral analysis

KW - Γ-convergence

UR - http://www.scopus.com/inward/record.url?scp=84863903931&partnerID=8YFLogxK

U2 - 10.1051/cocv/2011100

DO - 10.1051/cocv/2011100

M3 - Article

AN - SCOPUS:84863903931

SN - 1292-8119

VL - 18

SP - 427

EP - 451

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

IS - 2

ER -

Spectral analysis in a thin domain with periodically oscillating characteristics

Abstract

Keywords

ASJC Scopus subject areas

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