An introduction to the spectral asymptotics of a damped wave equation on metric graphs
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.
Supporting agencies: The research was supported by the project Development of postdoc activities at the University of Hradec Kr´alov´e, CZ.1.07/2.3.00/30.0015.
About the Author
J. Lipovsk´y
University of Hradec Kr´alov´e
Czech Republic
Czech Republic
Department of Physics, Faculty of Science
Rokitansk´eho 62, 500 03 Hradec Kr´alov´e
References
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Review
For citations:
Lipovsk´y J. An introduction to the spectral asymptotics of a damped wave equation on metric graphs. Nanosystems: Physics, Chemistry, Mathematics. 2015;6(2):182-191. https://doi.org/10.17586/2220-8054-2015-6-2-182-191
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