  In this paper, the Cauchy problem for a Friedrichs system on a globally
hyperbolic manifold with a timelike boundary is investigated. By imposing
admissible boundary conditions, the existence and the uniqueness of strong
solutions are shown. Furthermore, if the Friedrichs system is hyperbolic, the
Cauchy problem is proved to be well-posed in the sense of Hadamard. Finally,
examples of Friedrichs systems with admissible boundary conditions are
provided. Keywords: symmetric hyperbolic systems, symmetric positive systems,
admissible boundary conditions, Dirac operator, normally hyperbolic operator,
Klein-Gordon operator, heat operator, reaction-diffusion operator, globally
hyperbolic manifolds with timelike boundary.
