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).
Scopus subject areas
- Statistics and Probability
- Computer Science Applications
- Applied Mathematics