Geometry of wave damping on the torus
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915530320904192 |
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| author | Datchev, Kiril Kleinhenz, Perry Prouff, Antoine |
| author_facet | Datchev, Kiril Kleinhenz, Perry Prouff, Antoine |
| contents | Energy decay rates of damped waves on the torus depend on the behavior of the damping near the undamped region and on the geometry of the damped set. In this paper we refine these geometric considerations, by introducing the concept of order of a glancing undamped point, and estimating decay rates in terms of this order. The proof is based on generalizing an averaging argument due to Sun. We also show that damping sets which attain these improvements are generic among polygons and smooth curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05239 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometry of wave damping on the torus Datchev, Kiril Kleinhenz, Perry Prouff, Antoine Analysis of PDEs Mathematical Physics Energy decay rates of damped waves on the torus depend on the behavior of the damping near the undamped region and on the geometry of the damped set. In this paper we refine these geometric considerations, by introducing the concept of order of a glancing undamped point, and estimating decay rates in terms of this order. The proof is based on generalizing an averaging argument due to Sun. We also show that damping sets which attain these improvements are generic among polygons and smooth curves. |
| title | Geometry of wave damping on the torus |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2509.05239 |