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

This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 765579

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  • We consider a port-Hamiltonian system on an open spatial domain $ \Omega \subseteq \mathbb{R}^n $ 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.

    Mathematics Subject Classification: 47D06, 93C20, 35Q93, 47F05.

    Citation:

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  • Figure 1.  Illustration of a quasi Gelfand triple, where $ D_{+} = \text{dom} \ \iota_{+} $ and $ D_{-} = \text{dom} \ \iota_{-} $

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