## Abstract

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).

Original language | English |
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Pages (from-to) | 733–757 |

Journal | Networks and Heterogeneous Media |

Volume | 14 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2019 |

## Scopus subject areas

- Statistics and Probability
- Engineering(all)
- Computer Science Applications
- Applied Mathematics