Remark on justification of asymptotics of spectra of cylindrical waveguides with periodic singular perturbations of boundary and coefficients

DOI10.1007/s10958-021-05506-zzbMath1472.35258OpenAlexW3196850974MaRDI QIDQ1983991

M.-E. Pérez-Martínez, Delfina Gómez, Sergueï A. Nazarov, Rafael Orive-Illera

Publication date: 13 September 2021

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-021-05506-z

zbMATH Keywords

Floquet-Bloch theoryperiodically perforated waveguide

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (2)

Spectral gaps in a double-periodic perforated Neumann waveguide ⋮ Asymptotic stability of the spectrum of a parametric family of homogenization problems associated with a perforated waveguide

Cites Work

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• Gap opening and split band edges in waveguides coupled by a periodic system of small windows
• The localization for eigenfunctions of the Dirichlet problem in thin polyhedra near the vertices
• Opening of a gap in the continuous spectrum of a periodically perturbed waveguide
• Convergence of spectra of graph-like thin manifolds
• Gap in the essential spectrum of an elliptic formally self-adjoint system of differential equations
• Spectral analysis on graph-like spaces
• Gaps in the spectrum of a waveguide composed of domains with different limiting dimensions
• On the spectrum of narrow periodic waveguides
• Elliptic problems in domains with piecewise smooth boundaries
• Band gap of the spectrum in periodically curved quantum waveguides
• Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Vol. II. Transl. from the German by Boris Plamenevskii
• Asymptotic structure of the spectrum in a Dirichlet-strip with double periodic perforations
• Localization effect for Dirichlet eigenfunctions in thin non-smooth domains
• A gap in the spectrum of the Neumann–Laplacian on a periodic waveguide
• On spectrum gaps of some divergent elliptic operators with periodic coefficients
• The polynomial property of self-adjoint elliptic boundary-value problems and an algebraic description of their attributes
• Spectral properties of periodic media in the large coupling limit
• Spectral gaps for the Dirichlet‐Laplacian in a 3‐D waveguide periodically perturbed by a family of concentrated masses
• JUSTIFICATION OF ASYMPTOTIC EXPANSIONS OF THE EIGENVALUES OF NONSELFADJOINT SINGULARLY PERTURBED ELLIPTIC BOUNDARY VALUE PROBLEMS
• The stiff Neumann problem: Asymptotic specialty and “kissing” domains
• Essential spectrum of a periodic elastic waveguide may contain arbitrarily many gaps
• Spectral gaps for water waves above a corrugated bottom
• Floquet theory for partial differential equations

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