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

Abstract

<p style='text-indent:20px;'>We consider a port-Hamiltonian system on an open spatial domain <inline-formula><tex-math id="M1">\begin{document}$ \Omega \subseteq \mathbb{R}^n $\end{document}</tex-math></inline-formula> with bounded Lipschitz boundary. We show that there is a boundary triple associated to this system. Hence, we can characterize all boundary conditions that provide unique solutions that are non-increasing in the Hamiltonian. As a by-product we develop the theory of quasi Gelfand triples. Adding "natural" boundary controls and boundary observations yields scattering/impedance passive boundary control systems. This framework will be applied to the wave equation, Maxwell's equations and Mindlin plate model. Probably, there are even more applications.</p>