A control-based spatial source reconstruction in fractional heat equations
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914095845867520 |
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| author | García, Galina Vidal, Joaquín Zamorano, Sebastián |
| author_facet | García, Galina Vidal, Joaquín Zamorano, Sebastián |
| contents | This article addresses the inverse source problem for a nonlocal heat equation involving the fractional Laplacian. The primary goal is to reconstruct the spatial component of the source term from partial observations of the system's state and its time derivative over a subset of the domain. A reconstruction formula for the Fourier coefficients of the unknown source is derived, leveraging the null controllability property of the fractional heat equation when the fractional order lies in the interval $s\in(1/2,1)$. The methodology builds on spectral analysis and Volterra integral equations, providing a robust framework for recovering spatial sources under limited measurement data. Numerical experiments confirm the accuracy and stability of the proposed approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07528 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A control-based spatial source reconstruction in fractional heat equations García, Galina Vidal, Joaquín Zamorano, Sebastián Numerical Analysis Optimization and Control This article addresses the inverse source problem for a nonlocal heat equation involving the fractional Laplacian. The primary goal is to reconstruct the spatial component of the source term from partial observations of the system's state and its time derivative over a subset of the domain. A reconstruction formula for the Fourier coefficients of the unknown source is derived, leveraging the null controllability property of the fractional heat equation when the fractional order lies in the interval $s\in(1/2,1)$. The methodology builds on spectral analysis and Volterra integral equations, providing a robust framework for recovering spatial sources under limited measurement data. Numerical experiments confirm the accuracy and stability of the proposed approach. |
| title | A control-based spatial source reconstruction in fractional heat equations |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2510.07528 |