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Nanosystems: Physics, Chemistry, Mathematics, 2015, Volume 6, Issue 2, Pages 182–191
DOI: https://doi.org/10.17586/2220-8054-2015-6-2-182-191 (Mi nano931) 		 
An introduction to the spectral asymptotics of a damped wave equation on metric graphs

J. Lipovský

Department of Physics, Faculty of Science, University of Hradec Králové, Rokitanského 62, 500 03 Hradec Králové, Czechia
Full-text PDF (298 kB)
DOI: https://doi.org/10.17586/2220-8054-2015-6-2-182-191
Abstract: This paper summarizes the main results of [1] for the spectral asymptotics of the damped wave equation. We define the notion of a high frequency abscissa, a sequence of eigenvalues with imaginary parts going to plus or minus infinity and real parts going to some real number. We give theorems on the number of such high frequency abscissas for particular conditions on the graph. We illustrate this behavior in two particular examples.
Keywords: damped wave equation, spectrum, metric graphs.
Funding agency Grant number
University of Hradec Kralove CZ.1.07/2.3.00/30.0015
The research was supported by the project Development of postdoc activities at the University of Hradec Králové, CZ.1.07/2.3.00/30.0015.
Received: 02.02.2015
Bibliographic databases:
Document Type: Article
PACS: 03.65.Db, 03.65.Ge
Language: English
Citation: J. Lipovský, “An introduction to the spectral asymptotics of a damped wave equation on metric graphs”, Nanosystems: Physics, Chemistry, Mathematics, 6:2 (2015), 182–191
Citation in format AMSBIB
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\by J.~Lipovsk\'y
\paper An introduction to the spectral asymptotics of a damped wave equation on metric graphs
\jour Nanosystems: Physics, Chemistry, Mathematics
\yr 2015
\vol 6
\issue 2
\pages 182--191
\mathnet{http://mi.mathnet.ru/nano931}
\crossref{https://doi.org/10.17586/2220-8054-2015-6-2-182-191}
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\elib{https://elibrary.ru/item.asp?id=23238120}
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