Spatio-temporal responses of a class of 2×2 hyperbolic systems

Results of the spatio-temporal analysis of a class of distributed parameter systems described by hyperbolic partial differential equations defined on a one-dimensional spatial domain are presented. For the case of the two boundary inputs of Dirichlet type applied at the same point of the spatial domain, the analytical expressions for the impulse response functions are derived based on the inverse Laplace transform of individual elements of the 2×2 transfer function matrix. The considerations are illustrated with a practical example of a coaxial heat exchanger operating in parallel-flow mode which correspond to the analyzed boundary conditions.