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 journalArticlepeer-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 languageEnglish (US)
Pages (from-to)427-451
Number of pages25
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume18
Issue number2
DOIs
StatePublished - Apr 1 2012

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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