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

Sergei A. Nazarov, Rafael Orive-Illera, Maria-Eugenia Perez-Martinez

Research output

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 languageEnglish
Pages (from-to)733–757
JournalNetworks and Heterogeneous Media
Volume14
Issue number4
DOIs
Publication statusPublished - 2019

Scopus subject areas

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

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