Unique and Stable Recovery of Space-Variable Order in Multidimensional Subdiffusion
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914221532381184 |
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| author | Hong, Jiho Jin, Bangti Kian, Yavar |
| author_facet | Hong, Jiho Jin, Bangti Kian, Yavar |
| contents | In this work we investigate the unique identifiability and stable recovery of a spatially dependent variable-order in the subdiffusion model from the boundary flux measurement. We establish several new unique identifiability results from the observation at one point on the boundary without / with the knowledge of medium properties, and a conditional Lipschitz stability estimate when the observation is available on the whole boundary. The analysis crucially employs resolvent estimates in the $L^r(Ω)$ ($r>d$) spaces, solution representation in the Laplace domain and novel asymptotic expansions of the Laplace transform of the boundary flux at $p= 0$ and $p=1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06524 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unique and Stable Recovery of Space-Variable Order in Multidimensional Subdiffusion Hong, Jiho Jin, Bangti Kian, Yavar Analysis of PDEs In this work we investigate the unique identifiability and stable recovery of a spatially dependent variable-order in the subdiffusion model from the boundary flux measurement. We establish several new unique identifiability results from the observation at one point on the boundary without / with the knowledge of medium properties, and a conditional Lipschitz stability estimate when the observation is available on the whole boundary. The analysis crucially employs resolvent estimates in the $L^r(Ω)$ ($r>d$) spaces, solution representation in the Laplace domain and novel asymptotic expansions of the Laplace transform of the boundary flux at $p= 0$ and $p=1$. |
| title | Unique and Stable Recovery of Space-Variable Order in Multidimensional Subdiffusion |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.06524 |