A gap in the spectrum of the Neumann–Laplacian on a periodic waveguide

DOI10.1080/00036811.2012.711819zbMath1302.35266arXiv1110.5990OpenAlexW1981731288WikidataQ58245378 ScholiaQ58245378MaRDI QIDQ2846766

Fedor L. Bakharev, Sergueï A. Nazarov, Keijo Matti Ruotsalainen

Publication date: 3 September 2013

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.5990

zbMATH Keywords

Helmholtz equationspectral gapsperiodic waveguidesingularly perturbed domains

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (14)

Spectral gaps in a double-periodic perforated Neumann waveguide ⋮ Spectrum of a singularly perturbed periodic thin waveguide ⋮ Geometrically induced spectral effects in tubes with a mixed Dirichlet-Neumann boundary ⋮ Gap opening and split band edges in waveguides coupled by a periodic system of small windows ⋮ Opening up and control of spectral gaps of the Laplacian in periodic domains ⋮ Asymptotic stability of the spectrum of a parametric family of homogenization problems associated with a perforated waveguide ⋮ Bands in the spectrum of a periodic elastic waveguide ⋮ Spectral gaps for periodic piezoelectric waveguides ⋮ The asymptotic analysis of gaps in the spectrum of a waveguide perturbed with a periodic family of small voids ⋮ Remark on justification of asymptotics of spectra of cylindrical waveguides with periodic singular perturbations of boundary and coefficients ⋮ Essential spectrum of a periodic waveguide with non-periodic perturbation ⋮ Spectral gaps in the Dirichlet and Neumann problems on the plane perforated by a doubleperiodic family of circular holes ⋮ Spectral properties of an elliptic operator with double-contrast coefficients near a hyperplane ⋮ Asymptotics of eigenvalues in spectral gaps of periodic waveguides with small singular perturbations

Cites Work

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• Band-Gap Structure of Spectra of Periodic Dielectric and Acoustic Media. I. Scalar Model
• Essential spectrum of a periodic elastic waveguide may contain arbitrarily many gaps
• Regular degeneration and boundary layer for linear differential equations with small parameter
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)

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