Pedro Freitas, Jiri Lipovsky
We consider the linear damped wave equation on finite metric graphs and analyse its spectral properties with an emphasys on the asymptotic behaviour of eigenvalues. In the case of equilateral edges and certain coupling conditions, we show that there is only a finite number of high frequency abscissas. We further describe some of the possible behaviour when the edges have comensurate lengths. In either case, we show that the location of these abscissas is solely determined by the averages of the damping terms on each edge.
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http://arxiv.org/abs/1307.6377
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