Spectral Convergence for High‐Contrast Elliptic Periodic Problems with a Defect Via Homogenization

DOI10.1112/S0025579300000942zbMath1196.35036arXiv0801.0084OpenAlexW2962800923MaRDI QIDQ3400765

Mikhail Cherdantsev

Publication date: 5 February 2010

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.0084

zbMATH Keywords

two-scale convergencestability of the essential spectrum

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Methods involving semicontinuity and convergence; relaxation (49J45) Second-order elliptic equations (35J15) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (10)

Application of the method of asymptotic homogenization to an acoustic metafluid ⋮ Extreme Localization of Eigenfunctions to One-Dimensional High-Contrast Periodic Problems with a Defect ⋮ Quasi-periodic two-scale homogenisation and effective spatial dispersion in high-contrast media ⋮ Localized modes due to defects in high contrast periodic media via two-scale homogenization ⋮ Resonance and double negative behavior in metamaterials ⋮ Convergence Rates for Defect Modes in Large Finite Resonator Arrays ⋮ Eigenfunctions Localised on a Defect in High-Contrast Random Media ⋮ Two-scale homogenization for a general class of high contrast PDE systems with periodic coefficients ⋮ Convergent Power Series for Fields in Positive or Negative High-Contrast Periodic Media ⋮ Defect Resonances of Truncated Crystal Structures

Cites Work

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• Derivation of the Double Porosity Model of Single Phase Flow via Homogenization Theory
• Magnetism and Homogenization of Microresonators
• Homogenization and Two-Scale Convergence
• A General Convergence Result for a Functional Related to the Theory of Homogenization
• Spectral properties of periodic media in the large coupling limit
• Homogenization of elasticity equations with contrasting coefficients
• Non-local homogenized limits for composite media with highly anisotropic periodic fibres

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