Spectral analysis of a class of linear hyperbolic partial differential equations

A class of linear hyperbolic partial differential equations, sometimes called networks of waves, is considered. For this class of systems, necessary and sufficient conditions are formulated on the system matrices for the operator dynamics to be a Riesz-spectral operator. In that case, its spectrum is computed explicitly, together with the corresponding eigenfunctions, which constitutes the main result of our note. In particular, this enables to characterize easily many different concepts, such as stability. We apply our results to characterize exponential stability of a co-current heat exchanger.