Integrated Local Energy Decay for Waves with Time-Dependent Damping
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917066694459392 |
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| author | Kleinhenz, Perry McNulty, Michael |
| author_facet | Kleinhenz, Perry McNulty, Michael |
| contents | We prove integrated local energy decay for solutions of the damped wave equation with time-dependent damping satisfying an appropriate generalization of the geometric control condition on asymptotically flat, stationary space-times. We first obtain a high frequency estimate, which we prove via a positive commutator estimate using an escape function explicitly constructed in terms of the damping around individual space-time trajectories. We combine the high frequency estimate with low and medium frequency results for the undamped problem, then we handle the damping term as a perturbation to obtain local energy decay. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integrated Local Energy Decay for Waves with Time-Dependent Damping Kleinhenz, Perry McNulty, Michael Analysis of PDEs Mathematical Physics We prove integrated local energy decay for solutions of the damped wave equation with time-dependent damping satisfying an appropriate generalization of the geometric control condition on asymptotically flat, stationary space-times. We first obtain a high frequency estimate, which we prove via a positive commutator estimate using an escape function explicitly constructed in terms of the damping around individual space-time trajectories. We combine the high frequency estimate with low and medium frequency results for the undamped problem, then we handle the damping term as a perturbation to obtain local energy decay. |
| title | Integrated Local Energy Decay for Waves with Time-Dependent Damping |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2510.00179 |