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

Authors

Abstract

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.

Citation

Journal: Evolution Equations and Control Theory
Year: 2021
Volume: 10
Issue: 4
Pages: 965–1006
Publisher: American Institute of Mathematical Sciences (AIMS)
DOI: 10.3934/eect.2020098

BibTeX

@article{Skrepek_2021,
  title={{Well-posedness of linear first order port-Hamiltonian Systems on multidimensional spatial domains}},
  volume={10},
  ISSN={2163-2480},
  DOI={10.3934/eect.2020098},
  number={4},
  journal={Evolution Equations and Control Theory},
  publisher={American Institute of Mathematical Sciences (AIMS)},
  author={Skrepek, Nathanael},
  year={2021},
  pages={965--1006}
}

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References

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