A universal example for quantitative semi-uniform stability
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917279798657024 |
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| author | Arora, Sahiba Schwenninger, Felix Vukusic, Ingrid Waurick, Marcus |
| author_facet | Arora, Sahiba Schwenninger, Felix Vukusic, Ingrid Waurick, Marcus |
| contents | We characterise quantitative semi-uniform stability for $C_0$-semigroups arising from port-Hamiltonian systems, complementing recent works on exponential and strong stability. With the result, we present a simple universal example class of port-Hamiltonian $C_0$-semigroups exhibiting arbitrary decay rates slower than $t^{-1/2}$.
The latter is based on results from the theory of Diophantine approximation, as the decay rates will be strongly related to the approximation properties of irrational numbers by rationals obtained from cut-offs of continued fraction expansions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02357 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A universal example for quantitative semi-uniform stability Arora, Sahiba Schwenninger, Felix Vukusic, Ingrid Waurick, Marcus Analysis of PDEs Functional Analysis Number Theory Optimization and Control 35B35, 93D20, 35L04, 11Jxx We characterise quantitative semi-uniform stability for $C_0$-semigroups arising from port-Hamiltonian systems, complementing recent works on exponential and strong stability. With the result, we present a simple universal example class of port-Hamiltonian $C_0$-semigroups exhibiting arbitrary decay rates slower than $t^{-1/2}$. The latter is based on results from the theory of Diophantine approximation, as the decay rates will be strongly related to the approximation properties of irrational numbers by rationals obtained from cut-offs of continued fraction expansions. |
| title | A universal example for quantitative semi-uniform stability |
| topic | Analysis of PDEs Functional Analysis Number Theory Optimization and Control 35B35, 93D20, 35L04, 11Jxx |
| url | https://arxiv.org/abs/2410.02357 |