Determining a time‐varying potential in time‐fractional diffusion from observation at a single point
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Wiley Open Access
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| Natura: | Artículo Open Access |
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Wiley
2024
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| author | Siyu Cen Kwancheol Shin Zhi Zhou |
| author_facet | Siyu Cen Kwancheol Shin Zhi Zhou Siyu Cen Kwancheol Shin Zhi Zhou |
| collection | Wiley Open Access |
| contents | Determining a time‐varying potential in time‐fractional diffusion from observation at a single point Siyu Cen Kwancheol Shin Zhi Zhou Numerical Methods for Partial Differential Equations AbstractWe discuss the identification of a time‐dependent potential in a time‐fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem. Numerically, we develop an easily implementable iterative algorithm to recover the unknown coefficient, and also derive rigorous error bounds for the discrete reconstruction. These results are attained by leveraging the (discrete) solution theory of direct problems, and applying error estimates that are optimal with respect to problem data regularity. Numerical simulations are provided to demonstrate the theoretical results. 10.1002/num.23136 http://creativecommons.org/licenses/by-nc/4.0/ |
| doi_str_mv | 10.1002/num.23136 |
| format | Artículo Open Access |
| id | wiley_oa_10_1002_num_23136 |
| institution | Wiley Open Access |
| license_str_mv | http://creativecommons.org/licenses/by-nc/4.0/ |
| publishDate | 2024 |
| publisher | Wiley |
| record_format | wiley_oa |
| spellingShingle | Determining a time‐varying potential in time‐fractional diffusion from observation at a single point Siyu Cen Kwancheol Shin Zhi Zhou Numerical Methods for Partial Differential Equations Determining a time‐varying potential in time‐fractional diffusion from observation at a single point Siyu Cen Kwancheol Shin Zhi Zhou Numerical Methods for Partial Differential Equations AbstractWe discuss the identification of a time‐dependent potential in a time‐fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem. Numerically, we develop an easily implementable iterative algorithm to recover the unknown coefficient, and also derive rigorous error bounds for the discrete reconstruction. These results are attained by leveraging the (discrete) solution theory of direct problems, and applying error estimates that are optimal with respect to problem data regularity. Numerical simulations are provided to demonstrate the theoretical results. 10.1002/num.23136 http://creativecommons.org/licenses/by-nc/4.0/ |
| title | Determining a time‐varying potential in time‐fractional diffusion from observation at a single point |
| topic | Numerical Methods for Partial Differential Equations |
| url | https://onlinelibrary.wiley.com/doi/10.1002/num.23136 |