Well-posedness of linear first order port-Hamiltonian Systems on multidimensional spatial domains

We consider a port-Hamiltonian system on spatial domain $\Omega \subseteq \mathbb{R}^n$ that is bounded with Lipschitz boundary. show there boundary triple associated to this system. Hence, we can characterize all conditions provide unique solutions are non-increasing in the Hamiltonian. As by-product develop theory of quasi Gelfand triples. Adding ``natural'' controls and observations yields scattering/impedance passive control systems. This framework be applied wave equation, Maxwell equations Mindlin plate model, probably many more.