Polynomial Stability of Non-Linearly Damped Contraction Semigroups
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arXiv
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| Format: | Preprint |
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2025
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| author | Paunonen, Lassi Seifert, David |
| author_facet | Paunonen, Lassi Seifert, David |
| contents | We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and suitable conditions on the non-linearity. We illustrate the strength of our abstract results by applying them to a one-dimensional wave equation with weak non-linear damping and to an Euler-Bernoulli beam with a tip mass subject to non-linear damping. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_04275 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polynomial Stability of Non-Linearly Damped Contraction Semigroups Paunonen, Lassi Seifert, David Functional Analysis Analysis of PDEs Optimization and Control 34G20, 47H20, 93D15, 93D20, 93B07 (47D06, 35B35, 35L20) We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and suitable conditions on the non-linearity. We illustrate the strength of our abstract results by applying them to a one-dimensional wave equation with weak non-linear damping and to an Euler-Bernoulli beam with a tip mass subject to non-linear damping. |
| title | Polynomial Stability of Non-Linearly Damped Contraction Semigroups |
| topic | Functional Analysis Analysis of PDEs Optimization and Control 34G20, 47H20, 93D15, 93D20, 93B07 (47D06, 35B35, 35L20) |
| url | https://arxiv.org/abs/2509.04275 |