Simultaneous uniqueness for a coefficient inverse problem in one-dimensional fractional diffusion equation from an interior point measurement
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914983687749632 |
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| author | Jing, Xiaohua Li, Zhiyuan Yamamoto, Masahiro |
| author_facet | Jing, Xiaohua Li, Zhiyuan Yamamoto, Masahiro |
| contents | This article is concerned with an inverse problem of simultaneously determining a spatially varying coefficient and a Robin coefficient for a one-dimensional fractional diffusion equation with a time-fractional derivative of order $α\in(0,1)$. We prove the uniqueness for the inverse problem by observation data at one interior point over a finite time interval, provided that a coefficient is known on a subinterval. Our proof is based on the uniqueness in the inverse spectracl problem for a Sturm-Liouville problem by means of the Weyl $m$-function and the spectral representation of the solution to an initial-boundary value problem for the fractional diffusion equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16808 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simultaneous uniqueness for a coefficient inverse problem in one-dimensional fractional diffusion equation from an interior point measurement Jing, Xiaohua Li, Zhiyuan Yamamoto, Masahiro Analysis of PDEs This article is concerned with an inverse problem of simultaneously determining a spatially varying coefficient and a Robin coefficient for a one-dimensional fractional diffusion equation with a time-fractional derivative of order $α\in(0,1)$. We prove the uniqueness for the inverse problem by observation data at one interior point over a finite time interval, provided that a coefficient is known on a subinterval. Our proof is based on the uniqueness in the inverse spectracl problem for a Sturm-Liouville problem by means of the Weyl $m$-function and the spectral representation of the solution to an initial-boundary value problem for the fractional diffusion equation. |
| title | Simultaneous uniqueness for a coefficient inverse problem in one-dimensional fractional diffusion equation from an interior point measurement |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.16808 |