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
|Author:||Chiadò Piat, Valeria1; Nazarov, Sergey A.2,3; Ruotsalainen, Keijo M.4|
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
|Online Access:||PDF Full Text (PDF, 0.2 MB)|
|Persistent link:|| http://urn.fi/urn:nbn:fi-fe2018080933564
|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.
|Pages:||321 - 342|
|Type of Publication:||
A1 Journal article – refereed
|Field of Science:||
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.
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