Asymptotics of eigenvalues in spectral gaps under regular perturbations of walls of a periodic waveguide
type: Item
instance of: scholarly article
title: Asymptotics of eigenvalues in spectral gaps under regular perturbations of walls of a periodic waveguide
zbMATH Open document ID: 1439.35145
published in: Journal of Mathematical Sciences (New York)
publication date: 2018-01-08T00:00:00Z
review text: The authors consider a two-dimensional periodic waveguide with a small localized perturbation. The waveguide is modeled by a two-dimensional cylinder with a periodically varying boundary. In this cylinder, the Dirichlet Laplacian is considered. A localized perturbation is a small localized variation of the boundary of the considered waveguide. The unperturbed operator has a pure essential spectrum, which has a band structure and can contain gaps. The perturbation keeps the essential spectrum unchanged but can generate isolated eigenvalues in the gaps. The main result of the paper describes the existence of such eigenvalues near the edges of the internal gaps and provides their asymptotics. Various cases of the structure of edges of the gaps are considered and their influence of the asymptotic behavior of the emerging eigenvalues is demonstrated.
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 81R12
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35P05
zbMATH DE Number: 6822967
zbMATH Keywords: periodic waveguide
zbMATH Keywords: intrernal gaps
zbMATH Keywords: emerging eigenvalues
author: Sergei A. Nazarov
reviewed by: Denis Borisov
MaRDI profile type: Publication
full work available at URL: s10958-017-3542-x
OpenAlex ID: W2754621415
cites work: The boundary value problems of mathematical physics. Transl. from the Russian by Jack Lohwater
cites work: Q5796198
cites work: Floquet theory for partial differential equations
cites work: Elliptic problems in domains with piecewise smooth boundaries
cites work: ABSOLUTE CONTINUITY IN PERIODIC WAVEGUIDES
cites work: Q4436158
cites work: Quasiconformal mappings and periodic spectral problems in dimension two
cites work: Almost standing waves in a periodic waveguide with resonator, and near-threshold eigenvalues
cites work: Variational and asymptotic methods for finding eigenvalues below the continuous spectrum threshold
cites work: Asymptotic expansions of eigenvalues in the continuous spectrum of a regularly perturbed quantum waveguide
cites work: Enforced stability of a simple eigenvalue in the continuous spectrum of a waveguide
cites work: Q3993197
cites work: Q5628582
cites work: Q5526485
cites work: Homogenization of eigenvalue problems in perforated domains
cites work: Opening of a gap in the continuous spectrum of a periodically perturbed waveguide
cites work: A gap in the essential spectrum of a cylindrical waveguide with a periodic perturbation of the surface
cites work: The asymptotic analysis of gaps in the spectrum of a waveguide perturbed with a periodic family of small voids
cites work: Gap opening and split band edges in waveguides coupled by a periodic system of small windows
cites work: ELLIPTIC BOUNDARY VALUE PROBLEMS WITH PERIODIC COEFFICIENTS IN A CYLINDER
cites work: Properties of Spectra of Boundary Value Problems in Cylindrical and Quasicylindrical Domains
cites work: Q5579945
cites work: Q5571194
cites work: Q3743666
cites work: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
cites work: Q5509552
cites work: Q3994682
cites work: Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Vol. II. Transl. from the German by Boris Plamenevskii
cites work: On the spectrum of the Laplace operator on an infinite Dirichlet lattice
cites work: Localization estimates for eigenfrequencies of waves trapped by a freely floating body in a channel
DOI: 10.1007/S10958-017-3542-X
description: scientific article; zbMATH DE number 6822967