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

Abstract

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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.

How to cite

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Ferreira, 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 &lt; 1), or ε is much greater than δ(δ = ετ, τ &gt; 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 &lt; 1), or ε is much greater than δ(δ = ετ, τ &gt; 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 -

References

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