Inverse source problem with a posteriori interior measurements for space-time fractional diffusion equations
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917035088281600 |
|---|---|
| author | Yu, Kai Li, Zhiyuan Liu, Yikan |
| author_facet | Yu, Kai Li, Zhiyuan Liu, Yikan |
| contents | This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique continuation property. For the numerical reconstruction, the inverse problem is reformulated as an optimization problem with the Tikhonov regularization. We use the Levenberg-Marquardt method to identity the unknown source from noisy measurements. Finally, we give some numerical examples to illustrate the efficiency and accuracy of the proposed algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21070 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse source problem with a posteriori interior measurements for space-time fractional diffusion equations Yu, Kai Li, Zhiyuan Liu, Yikan Numerical Analysis 35R30, 35R11 This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique continuation property. For the numerical reconstruction, the inverse problem is reformulated as an optimization problem with the Tikhonov regularization. We use the Levenberg-Marquardt method to identity the unknown source from noisy measurements. Finally, we give some numerical examples to illustrate the efficiency and accuracy of the proposed algorithm. |
| title | Inverse source problem with a posteriori interior measurements for space-time fractional diffusion equations |
| topic | Numerical Analysis 35R30, 35R11 |
| url | https://arxiv.org/abs/2506.21070 |