TY - JOUR

T1 - Asymptotic structure of the spectrum in a dirichlet-strip with double periodic perforations

AU - Nazarov, Sergei A.

AU - Orive-Illera, Rafael

AU - Perez-Martinez, Maria-Eugenia

PY - 2019

Y1 - 2019

N2 - We address a spectral problem for the Dirichlet-Laplace operator in a waveguide II ε. II ε is obtained from an unbounded two-dimensional strip II which is periodically perforated by a family of holes, which are also periodically distributed along a line, the so-called "perforation string". We assume that the two periods are different, namely, O(1) and O( ε) respectively, where 0 < ε ≪ 1. We look at the band-gap structure of the spectrum σ ε as ε → 0. We derive asymptotic formulas for the endpoints of the spectral bands and show that σ ε has a large number of short bands of length O( ε) which alternate with wide gaps of width O(1).

AB - We address a spectral problem for the Dirichlet-Laplace operator in a waveguide II ε. II ε is obtained from an unbounded two-dimensional strip II which is periodically perforated by a family of holes, which are also periodically distributed along a line, the so-called "perforation string". We assume that the two periods are different, namely, O(1) and O( ε) respectively, where 0 < ε ≪ 1. We look at the band-gap structure of the spectrum σ ε as ε → 0. We derive asymptotic formulas for the endpoints of the spectral bands and show that σ ε has a large number of short bands of length O( ε) which alternate with wide gaps of width O(1).

KW - Band-gap structure

KW - Dirichlet-Laplace operator

KW - Double periodicity

KW - Homogenization

KW - Perforated media

KW - Spectral perturbations

UR - http://www.scopus.com/inward/record.url?scp=85075594129&partnerID=8YFLogxK

U2 - 10.3934/nhm.2019029

DO - 10.3934/nhm.2019029

M3 - Article

VL - 14

SP - 733

EP - 757

JO - Networks and Heterogeneous Media

JF - Networks and Heterogeneous Media

SN - 1556-1801

IS - 4

ER -