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Applicable Analysis
An International Journal
Volume 89, 2010 - Issue 1
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Original Articles

Essential spectrum of a periodic elastic waveguide may contain arbitrarily many gaps

Sergey A. Nazarov Institute of Mechanical Engineering Problems, V.O., Bolshoi pr., 61, 199178, St. Petersburg, Russia
,
Keijo Ruotsalainen Department of Electrical and Information Engineering, Mathematics Division, University of Oulu, P.O. Box 4500, FI-90401 Oulu, Finland
&
Jari Taskinen Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014 Helsinki, FinlandCorrespondence[email protected]
Pages 109-124 | Received 15 Sep 2009, Accepted 06 Nov 2009, Published online: 19 Jan 2010

Citations (19)

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Read on this site (2)

L. D'Elia & S.A. Nazarov. (2023) Gaps in the spectrum of two-dimensional square packing of stiff disks. Applicable Analysis 102:9, pages 2611-2627.
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F.L. Bakharev, S.A. Nazarov & K.M. Ruotsalainen. (2013) A gap in the spectrum of the Neumann–Laplacian on a periodic waveguide. Applicable Analysis 92:9, pages 1889-1915.
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Articles from other publishers (17)

Marcus Rosenberg & Jari Taskinen. (2024) Some aspects of the Floquet theory for the heat equation in a periodic domain. Journal of Evolution Equations 24:2.
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Delfina Gómez, Sergei A. Nazarov, Rafael Orive-Illera & María-Eugenia Pérez-Martínez. (2023) Spectral gaps in a double-periodic perforated Neumann waveguide. Asymptotic Analysis 131:3-4, pages 385-441.
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Jari Taskinen. 2023. Operators, Semigroups, Algebras and Function Theory. Operators, Semigroups, Algebras and Function Theory 199 224 .
D. Gómez, S. A. Nazarov, R. Orive-Illera & M.-E. Pérez-Martínez. (2021) Remark on Justification of Asymptotics of Spectra of Cylindrical Waveguides with Periodic Singular Perturbations of Boundary and Coefficients. Journal of Mathematical Sciences 257:5, pages 597-623.
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S. A. Nazarov. (2020) Anomalies of Acoustic Wave Scattering Near the Cut-off Points of Continuous Spectrum (A Review). Acoustical Physics 66:5, pages 477-494.
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Sergei A. Nazarov & Jari Taskinen. (2018) Essential spectrum of a periodic waveguide with non-periodic perturbation. Journal of Mathematical Analysis and Applications 463:2, pages 922-933.
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D. Gómez, S. A. Nazarov & M. E. Pérez. (2018) Homogenization of Winkler–Steklov spectral conditions in three-dimensional linear elasticity. Zeitschrift für angewandte Mathematik und Physik 69:2.
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Giuseppe Cardone & Andrii Khrabustovskyi. (2017) Spectrum of a singularly perturbed periodic thin waveguide. Journal of Mathematical Analysis and Applications 454:2, pages 673-694.
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F. L. Bakharev & J. Taskinen. (2017) Bands in the spectrum of a periodic elastic waveguide. Zeitschrift für angewandte Mathematik und Physik 68:5.
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Sergei A. Nazarov & Jari Taskinen. (2016) Elastic and piezoelectric waveguides may have infinite number of gaps in their spectra. Comptes Rendus. Mécanique 344:3, pages 190-194.
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Sergei A. Nazarov & Jari Taskinen. (2015) Spectral gaps for periodic piezoelectric waveguides. Zeitschrift für angewandte Mathematik und Physik 66:6, pages 3017-3047.
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S. A. Nazarov. (2015) Eigenmodes of a thin elastic layer between periodic rigid profiles. Computational Mathematics and Mathematical Physics 55:10, pages 1684-1697.
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S. A. Nazarov. (2015) Gap Opening Around a Given Point of the Spectrum of a Cylindrical Waveguide by Means of a Gentle Periodic Perturbation of Walls. Journal of Mathematical Sciences 206:3, pages 288-314.
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Andrii Khrabustovskyi. (2014) Opening up and control of spectral gaps of the Laplacian in periodic domains. Journal of Mathematical Physics 55:12.
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S. A. Nazarov & J. Taskinen. (2013) Structure of the Spectrum of a Periodic Family of Identical Cells Connected by Converging Apertures. Journal of Mathematical Sciences 194:1, pages 72-82.
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F. L. Bakharev. (2013) Spectral gaps in the Dirichlet problem for the biharmonic operator on a plane periodically perforated by circular holes. Vestnik St. Petersburg University: Mathematics 46:2, pages 76-84.
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S. A. Nazarov, K. Ruotsalainen & J. Taskinen. (2012) Spectral gaps in the dirichlet and neumann problems on the plane perforated by a doubleperiodic family of circular holes. Journal of Mathematical Sciences 181:2, pages 164-222.
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