Stability via closure relations with applications to dissipative and port-Hamiltonian systems
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866917709336281088 |
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| author | Glück, Jochen Jacob, Birgit Meyer, Annika Wyss, Christian Zwart, Hans |
| author_facet | Glück, Jochen Jacob, Birgit Meyer, Annika Wyss, Christian Zwart, Hans |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2212_12025 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stability via closure relations with applications to dissipative and port-Hamiltonian systems Glück, Jochen Jacob, Birgit Meyer, Annika Wyss, Christian Zwart, Hans Functional Analysis Optimization and Control 93D23, 37K40, 47D06, 34G10 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. |
| title | Stability via closure relations with applications to dissipative and port-Hamiltonian systems |
| topic | Functional Analysis Optimization and Control 93D23, 37K40, 47D06, 34G10 |
| url | https://arxiv.org/abs/2212.12025 |