TY - JOUR

T1 - A gap in the spectrum of the Neumann-Laplacian on a periodic waveguide

AU - Bakharev, F.L.

AU - Nazarov, S.A.

AU - Ruotsalainen, K.M.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Helmholtz equation

KW - periodic waveguide

KW - spectral gaps

KW - singularly perturbed domains

U2 - 10.1080/00036811.2012.711819

DO - 10.1080/00036811.2012.711819

M3 - Article

VL - 92

SP - 1889

EP - 1915

JO - Applicable Analysis

JF - Applicable Analysis

SN - 0003-6811

IS - 9

ER -