F. L. Bakharev

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

We study a spectral problem related to the Laplace operator in a singularly perturbed periodic waveguide. The waveguide is a quasi-cylinder which contains a periodic arrangement of inclusions. On the boundary of the waveguide, we consider both Neumann and Dirichlet conditions. We prove that provided the diameter of the inclusion is small enough the spectrum of Laplace operator contains band gaps, i.e. there are frequencies that do not propagate through the waveguide. The existence of the band gaps is verified using the asymptotic analysis of elliptic operators.

Bands in the spectrum of a periodic elastic waveguide

We study the spectral linear elasticity problem in an unbounded periodic waveguide, which consists of a sequence of identical bounded cells connected by thin ligaments of diameter of order

SPECTRAL GAPS FOR THE LINEAR SURFACE WAVE MODEL IN PERIODIC CHANNELS

h >0

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

h>0. The essential spectrum of the problem is known to have band-gap structure. We derive asymptotic formulas for the position of the spectral bands and gaps, as

The discrete spectrum of cross-shaped waveguides

h \rightarrow 0

Geometrically Induced Spectral Effects in Tubes with a Mixed Dirichlet—Neumann Boundary

h→0.