University of Oulu

Chiadò Piat Valeria, Nazarov Sergey, Ruotsalainen Keijo: Spectral gaps and non-Bragg resonances in a water channel. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), 321-342. doi: 10.4171/RLM/809

Spectral gaps and non-Bragg resonances in a water channel

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Author: Chiadò Piat, Valeria1; Nazarov, Sergey A.2,3; Ruotsalainen, Keijo M.4
Organizations: 1DISMA (Department of Mathematical Sciences), Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
2St. Petersburg State University, Universitetskaya nab., 7–9 St. Petersburg 199034, Russia
3Institute of Problems of Mechanical Engineering, V.O., Bolshoj pr., 61 St. Petersburg, 199178 Russia
4Applied and Computational Mathematics Research Group, University of Oulu, Pentti Kaiteran katu 1, Linnanmaa, Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.2 MB)
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Language: English
Published: European Mathematical Society Publishing House, 2018
Publish Date: 2018-08-09


In this paper the essential spectrum of the linear problem of water-waves on a 3d-channel with gently periodic bottom will be studied. We show that under a certain geometric condition on the bottom profile the essential spectrum has spectral gaps. In classical analysis of waveguides it is known that the Bragg resonances at the edges of the Brillouin zones create band gaps in the spectrum. Here we demonstrate that the band gaps can be opened also in the frequency range far from the Bragg resonances. The position and the length of the gaps are found out by applying an asymptotic analysis to the model problem in the periodicity cell.

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Series: Rendiconti Lincei. Matematica e applicazioni
ISSN: 1120-6330
ISSN-E: 1720-0768
ISSN-L: 1120-6330
Volume: 29
Issue: 2
Pages: 321 - 342
DOI: 10.4171/RLM/809
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: This research is supported by INDAM-GNAMPA. The second author was supported by the Russian Foundation of Basic Research grant 18-01-00325. The third author was supported by the Jenny and Antti Wihuri foundation.
Copyright information: © 2018 EMS Publishing House. All rights reserved. Published in this repository with the kind permission of the publisher.