TITLE

The asymptotic analysis of gaps in the spectrum of a waveguide perturbed with a periodic family of small voids

AUTHOR(S)
Nazarov, S.
PUB. DATE
October 2012
SOURCE
Journal of Mathematical Sciences;Oct2012, Vol. 186 Issue 2, p247
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We study the spectrum of the Dirichlet problem for the Laplace operator in a cylindrical waveguide with periodic family of small (of diameter ε > 0) voids. Based on the asymptotic analysis of eigenvalues of the problem in a singularly perturbed periodicity cell, we show that the waveguide spectrum contains gaps of width O( ε), i.e., we provide a rigorous mathematical justification of the effect of splitting of edges of spectral bands. We consider several variants of splitting (or their absence), present asymptotic formulas for the gap edges and formulate open questions. The results are illustrated by examples. Bibliography: 38 titles. Illustrations: 13 figures.
ACCESSION #
80235627

 

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