Long-time asymptotic estimate and a related inverse source problem for time-fractional wave equations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910286788689920 |
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| author | Huang, Xinchi Liu, Yikan |
| author_facet | Huang, Xinchi Liu, Yikan |
| contents | Lying between traditional parabolic and hyperbolic equations, time-fractional wave equations of order $α\in(1,2)$ in time inherit both decaying and oscillating properties. In this article, we establish a long-time asymptotic estimate for homogeneous time-fractional wave equations, which readily implies the strict positivity/negativity of the solution for $t\gg1$ under some sign conditions on initial values. As a direct application, we prove the uniqueness for a related inverse source problem on determining the temporal component. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_14762 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Long-time asymptotic estimate and a related inverse source problem for time-fractional wave equations Huang, Xinchi Liu, Yikan Analysis of PDEs Lying between traditional parabolic and hyperbolic equations, time-fractional wave equations of order $α\in(1,2)$ in time inherit both decaying and oscillating properties. In this article, we establish a long-time asymptotic estimate for homogeneous time-fractional wave equations, which readily implies the strict positivity/negativity of the solution for $t\gg1$ under some sign conditions on initial values. As a direct application, we prove the uniqueness for a related inverse source problem on determining the temporal component. |
| title | Long-time asymptotic estimate and a related inverse source problem for time-fractional wave equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2209.14762 |