Semigroup decay for the wave equation with unbounded damping
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912978605965312 |
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| author | Arnal, Antonio Gerhat, Borbala Royer, Julien Siegl, Petr |
| author_facet | Arnal, Antonio Gerhat, Borbala Royer, Julien Siegl, Petr |
| contents | We study the damped wave equation with a damping coefficient which is possibly singular and unbounded at infinity. In general, zero belongs to the spectrum of the corresponding generator, which prevents a uniform (exponential) decay for the energy. However, for initial conditions in a suitable subspace, a detailed analysis of the resolvent norm for low frequencies leads to sharp polynomial time-decay rates for the solution and its energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21805 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semigroup decay for the wave equation with unbounded damping Arnal, Antonio Gerhat, Borbala Royer, Julien Siegl, Petr Analysis of PDEs Mathematical Physics Functional Analysis We study the damped wave equation with a damping coefficient which is possibly singular and unbounded at infinity. In general, zero belongs to the spectrum of the corresponding generator, which prevents a uniform (exponential) decay for the energy. However, for initial conditions in a suitable subspace, a detailed analysis of the resolvent norm for low frequencies leads to sharp polynomial time-decay rates for the solution and its energy. |
| title | Semigroup decay for the wave equation with unbounded damping |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2603.21805 |