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 & Control Theory
- Year: 2021
- Volume: 10
- Issue: 4
- Pages: 965
- 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 & Control Theory},
publisher={American Institute of Mathematical Sciences (AIMS)},
author={Skrepek, Nathanael},
year={2021},
pages={965}
}
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