Identification of a Spatially-Dependent Variable Order in One-Dimensional Subdiffusion
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929606939901952 |
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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 an inverse problem of identifying a spatially variable order in the one-dimensional subdiffusion model from the boundary flux measurement. The model involves a generalized Caputo derivative in time, and arises in the mathematical modeling of anomalous diffusion in heterogeneous media. We prove the unique recovery of a monotone piecewise constant variable order and its range for known and unknown media, respectively. The analysis is based on a delicate asymptotic expansion of the Laplace transform of the data as $p\to0$, which is of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Identification of a Spatially-Dependent Variable Order in One-Dimensional Subdiffusion Hong, Jiho Jin, Bangti Kian, Yavar Analysis of PDEs In this work we investigate an inverse problem of identifying a spatially variable order in the one-dimensional subdiffusion model from the boundary flux measurement. The model involves a generalized Caputo derivative in time, and arises in the mathematical modeling of anomalous diffusion in heterogeneous media. We prove the unique recovery of a monotone piecewise constant variable order and its range for known and unknown media, respectively. The analysis is based on a delicate asymptotic expansion of the Laplace transform of the data as $p\to0$, which is of independent interest. |
| title | Identification of a Spatially-Dependent Variable Order in One-Dimensional Subdiffusion |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.02193 |