Stability via closure relations with applications to dissipative and port-Hamiltonian systems
Abstract
We consider differential operators $A$ that can be represented by means of a so-called closure relation in terms of a simpler operator $A_{\operatorname{ext}}$ defined on a larger space. We analyze how the spectral properties of $A$ and $A_{\operatorname{ext}}$ are related and give sufficient conditions for exponential stability of the semigroup generated by $A$ in terms of the semigroup generated by $A_{\operatorname{ext}}$. 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2022
- DOI:
- 10.48550/arXiv.2212.12025
- arXiv:
- arXiv:2212.12025
- Bibcode:
- 2022arXiv221212025G
- Keywords:
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- Mathematics - Functional Analysis;
- Mathematics - Optimization and Control;
- 93D23;
- 37K40;
- 47D06;
- 34G10
- E-Print:
- 31 pages