Stability via closure relations with applications to dissipative and port-Hamiltonian systems

Authors

Jochen Glück, Birgit Jacob, Annika Meyer, Christian Wyss, Hans Zwart

Abstract

We consider differential operators A that can be represented by means of a so-called closure relation in terms of a simpler operator \( A_{ {\text {ext} } } \) defined on a larger space. We analyse how the spectral properties of \( A \) and \( A_{ {\text {ext} } } \) are related and give sufficient conditions for exponential stability of the semigroup generated by \( A \) in terms of the semigroup generated by \( A_{ {\text {ext} } } \). As applications we study the long-term behaviour of a coupled wave–heat system on an interval, parabolic equations on bounded domains that are coupled by matrix-valued potentials, and of linear infinite-dimensional port-Hamiltonian systems with dissipation on an interval.

Keywords

Port-Hamiltonian systems; Closure relations; Exponential stability; \( C_0 \)-semigroups; 93D23; 37K40; 47D06; 34G10

Citation

• Journal: Journal of Evolution Equations
• Year: 2024
• Volume: 24
• Issue: 3
• Pages:
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s00028-024-00992-5

BibTeX

@article{Gl_ck_2024,
  title={{Stability via closure relations with applications to dissipative and port-Hamiltonian systems}},
  volume={24},
  ISSN={1424-3202},
  DOI={10.1007/s00028-024-00992-5},
  number={3},
  journal={Journal of Evolution Equations},
  publisher={Springer Science and Business Media LLC},
  author={Glück, Jochen and Jacob, Birgit and Meyer, Annika and Wyss, Christian and Zwart, Hans},
  year={2024}
}

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