Optimal boundary control of hyperbolic equations with pointwise state constraints

In this paper, we consider dynamic optimization problems for hyperbolic systems with boundary controls and pointwise state constraints. In contrast to parabolic dynamics, such systems have not been sufficiently studied in the literature. The reason is the lack of regularity in the case of hyperbolic dynamics. We present necessary optimality conditions for both Neumann and Dirichlet boundary control problems and discuss differences and relationships between them.