Stability Estimates for the Inverse Problem of Reconstructing Point sources in Parabolic Equations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908875630837760 |
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| author | Huang, Kuang Jin, Bangti Kian, Yavar Triki, Faouzi |
| author_facet | Huang, Kuang Jin, Bangti Kian, Yavar Triki, Faouzi |
| contents | In this work, we investigate the stability issue of the inverse problem of determining the locations and time-dependent amplitudes of point sources in a parabolic equation with a non-self adjoint elliptic operator from boundary observations. We derive different stability estimates for determining the locations and the amplitudes of the sources in the space, the plane as well as in dimension one. The analysis employs a novel approach that combines several different arguments, including the improved regularity of the solutions, the application of Carleman estimates, time extension of solutions, and construction of explicit solutions to the adjoint equations. Further we provide numerical reconstructions to complement the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09099 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stability Estimates for the Inverse Problem of Reconstructing Point sources in Parabolic Equations Huang, Kuang Jin, Bangti Kian, Yavar Triki, Faouzi Analysis of PDEs In this work, we investigate the stability issue of the inverse problem of determining the locations and time-dependent amplitudes of point sources in a parabolic equation with a non-self adjoint elliptic operator from boundary observations. We derive different stability estimates for determining the locations and the amplitudes of the sources in the space, the plane as well as in dimension one. The analysis employs a novel approach that combines several different arguments, including the improved regularity of the solutions, the application of Carleman estimates, time extension of solutions, and construction of explicit solutions to the adjoint equations. Further we provide numerical reconstructions to complement the theoretical findings. |
| title | Stability Estimates for the Inverse Problem of Reconstructing Point sources in Parabolic Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.09099 |