A universal example for quantitative semi-uniform stability

Sahiba Arora; Felix Schwenninger; Ingrid Vukusic; Marcus Waurick

doi:10.48550/arXiv.2410.02357

A universal example for quantitative semi-uniform stability

Sahiba Arora, Felix Schwenninger, Ingrid Vukusic, Marcus Waurick

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Abstract

We characterise quantitative semi-uniform stability for C0-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 C0-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 approximation properties of irrational numbers by rationals given through cut-offs of continued fraction expansions.

Original language	English
Publisher	ArXiv.org
Number of pages	22
DOIs	https://doi.org/10.48550/arXiv.2410.02357
Publication status	Published - 3 Oct 2024

Keywords

math.AP
math.FA
math.NT
math.OC
35B35, 93D20, 35L04, 11Jxx

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PreprintFinal published version, 322 KBLicence: Other

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abstract = "We characterise quantitative semi-uniform stability for C0-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 C0-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 approximation properties of irrational numbers by rationals given through cut-offs of continued fraction expansions.",

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AU - Waurick, Marcus

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AB - We characterise quantitative semi-uniform stability for C0-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 C0-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 approximation properties of irrational numbers by rationals given through cut-offs of continued fraction expansions.

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A universal example for quantitative semi-uniform stability

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Keywords

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