Local decay and asymptotic profile for the damped wave equation in the asymptotically Euclidean setting
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915126477586432 |
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| author | Fahs, Rayan Royer, Julien |
| author_facet | Fahs, Rayan Royer, Julien |
| contents | We prove local decay estimates for the wave equation in the asymptotically Euclidean setting. In even dimensions we go beyond the optimal decay by providing the large time asymptotic profile, given by a solution of the free wave equation. In odd dimensions, we improve the best known estimates. In particular, we get a decay rate that is better than what would be the optimal decay in even dimensions. The analysis mainly relies on a comparison of the corresponding resolvent with the resolvent of the free problem for low frequencies. Moreover, all the results hold for the damped wave equation with short range absorption index. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_17056 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local decay and asymptotic profile for the damped wave equation in the asymptotically Euclidean setting Fahs, Rayan Royer, Julien Analysis of PDEs Mathematical Physics Spectral Theory 47N50, 47A10, 35B40, 47B44, 35L05, 35J05 We prove local decay estimates for the wave equation in the asymptotically Euclidean setting. In even dimensions we go beyond the optimal decay by providing the large time asymptotic profile, given by a solution of the free wave equation. In odd dimensions, we improve the best known estimates. In particular, we get a decay rate that is better than what would be the optimal decay in even dimensions. The analysis mainly relies on a comparison of the corresponding resolvent with the resolvent of the free problem for low frequencies. Moreover, all the results hold for the damped wave equation with short range absorption index. |
| title | Local decay and asymptotic profile for the damped wave equation in the asymptotically Euclidean setting |
| topic | Analysis of PDEs Mathematical Physics Spectral Theory 47N50, 47A10, 35B40, 47B44, 35L05, 35J05 |
| url | https://arxiv.org/abs/2501.17056 |