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.
"On the Cauchy problem for Friedrichs systems on globally hyperbolic manifolds with timelike boundary." Adv. Differential Equations 27 (7/8) 497 - 542, July/August 2022. https://doi.org/10.57262/ade027-0708-497