An introduction to the spectral asymptotics of a damped wave equation on metric graphs

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.