Asymptotic structure of the spectrum in a Dirichlet-strip with double periodic perforations
Entity
UAM. Departamento de MatemáticasPublisher
American Institute of Mathematical Sciences (AIMS)Date
2019-12-01Citation
10.3934/nhm.2019029
Networks and Heterogeneous Media 14.4 (2019): 733-757
ISSN
1556-1801 (print); 1556-181X (online)DOI
10.3934/nhm.2019029Funded by
The first author is supported by Russian Foundation on Basic Research, grant 18-01-00325. The second author is supported by the Spanish MINECO through the “Severo Ochoa Programme for Centres of Excellence in RaD” (SEV-2015-0554) and MTM2017-89976-P. The third author is supported by the Spanish MINECO grant MTM2013- 44883-P and MICINN grant PGC2018-098178-B-I00Project
Gobierno de España. SEV-2015-0554; Gobierno de España. MTM2017-89976-P; Gobierno de España. MTM2013-44883-P; Gobierno de España. PGC2018-098178-B-I00Editor's Version
https://doi.org/10.3934/nhm.2019029Subjects
Homogenization; Band-Gap Structure; Dirichlet-Laplace Operator; Double Periodicity; Perforated Media; Spectral Perturbations; MatemáticasRights
© 2019 American Institute of Mathematical SciencesAbstract
We address a spectral problem for the Dirichlet-Laplace operator in a waveguide IIε. IIε 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 σε as ε → 0. We derive asymptotic formulas for the endpoints of the spectral bands and show that σε has a large number of short bands of length O(ε) which alternate with wide gaps of width O(1)
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Google Scholar:Nazarov, Sergei A.
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Orive Illera, Rafael
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Pérez-Martínez, María Eugenia
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