Archivio Istituzionale della RicercaIn this paper, the essential spectrum of the linear problem on water waves in a water layer and in a channel with a gently corrugated bottom is studied. We show that, under a certain geometric condition, the essential spectrum has spectral gaps. In other words, there exist intervals in the positive real semi-axis that are free of the spectrum but have their endpoints in it. The position and the length of the gaps are found out by applying an asymptotic analysis to the model problem in the periodicity cell.
Spectral gaps for water waves above a corrugated bottom / CHIADO' PIAT, Valeria; S., Nazarov; K., Ruotsalainen. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A. - ISSN 1364-5021. - ELETTRONICO. - 469:(2013). [10.1098/rspa.2012.0545]
Spectral gaps for water waves above a corrugated bottom
CHIADO' PIAT, Valeria;
2013
Abstract
In this paper, the essential spectrum of the linear problem on water waves in a water layer and in a channel with a gently corrugated bottom is studied. We show that, under a certain geometric condition, the essential spectrum has spectral gaps. In other words, there exist intervals in the positive real semi-axis that are free of the spectrum but have their endpoints in it. 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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https://hdl.handle.net/11583/2504327
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