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Abstract: We address a spectral problem for the Dirichlet-Laplace operator in a waveguide ????. ???? is obtained from repsilon an unbounded two-dimensional strip ?? 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)O(1) and O(?)O(?) respectively, where 0?10?1. We look at the band-gap structure of the spectrum ???? as ??0??0. We derive asymptotic formulas for the endpoints of the spectral bands and show that ???? has a large number of short bands of length O(?)O(?) which alternate with wide gaps of width O(1)O(1).
Fuente: Networks and Heterogeneous Media ; Volume 14, Issue 4, 1 December 2019, Pages 733-757
Publisher: American Institute of Mathematical Sciences
Publication date: 01/12/2019
No. of pages: 25
Publication type: Article
DOI: 10.3934/nhm.2019029
ISSN: 1556-1801,1556-181X
Spanish project: MTM2013- 44883-P
Publication Url: https://www.aimsciences.org/article/doi/10.3934/nhm.2019029
Consult in UCrea Read publication
NAZAROV, SERGEI A.
ORIVE-ILLERA, RAFAEL
MARIA EUGENIA PEREZ MARTINEZ
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