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 for the operator dynamics to generate a C_0-group. This property turns out to be equivalent to the Riesz-spectral nature of that operator. In that case, its spectrum is computed explicitly, leading to easily checkable stability conditions. We apply our results to characterize exponential stability of a co-current heat exchanger.