Effects of Rayleigh Waves on the Essential Spectrum in Perturbed Doubly Periodic Elliptic Problems

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http://hdl.handle.net/10138/312496

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Bakharev , F L , Cardone , G , Nazarov , S A & Taskinen , J 2017 , ' Effects of Rayleigh Waves on the Essential Spectrum in Perturbed Doubly Periodic Elliptic Problems ' , Integral Equations and Operator Theory , vol. 88 , no. 3 , pp. 373-386 . https://doi.org/10.1007/s00020-017-2379-5

Title: Effects of Rayleigh Waves on the Essential Spectrum in Perturbed Doubly Periodic Elliptic Problems
Author: Bakharev, F. L.; Cardone, G.; Nazarov, S. A.; Taskinen, J.
Contributor organization: Department of Mathematics and Statistics
Date: 2017-07
Language: eng
Number of pages: 14
Belongs to series: Integral Equations and Operator Theory
ISSN: 0378-620X
DOI: https://doi.org/10.1007/s00020-017-2379-5
URI: http://hdl.handle.net/10138/312496
Abstract: We give an example of a scalar second order differential operator in the plane with double periodic coefficients and describe its modification, which causes an additional spectral band in the essential spectrum. The modified operator is obtained by applying to the coefficients a mirror reflection with respect to a vertical or horizontal line. This change gives rise to Rayleigh type waves localized near the line. The results are proven using asymptotic analysis, and they are based on high contrast of the coefficient functions.
Subject: Periodic media
Open waveguides
High contrast of coefficients
Asymptotics
Spectral bands
DIFFERENTIAL-EQUATIONS
RADIATION CONDITIONS
GUIDES
MEDIA
111 Mathematics
Peer reviewed: Yes
Usage restriction: openAccess
Self-archived version: acceptedVersion


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