A monotone iterative reconstruction method for an inverse drift problem in a two-dimensional parabolic equation
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917409618657280 |
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| author | Zhang, Liuying Zhang, Wenlong Zhang, Zhidong |
| author_facet | Zhang, Liuying Zhang, Wenlong Zhang, Zhidong |
| contents | We study an inverse drift problem for a two-dimensional parabolic equation on the unit square with mixed boundary conditions, where the drift coefficient is recovered from terminal observation data $g=u(\cdot,T)$. A monotone operator is constructed whose fixed point coincides with the unknown drift, yielding uniqueness in an admissible class and a constructive iterative reconstruction scheme. Numerical experiments illustrate the monotone convergence and the effectiveness of the proposed method, and show that it remains effective for noisy terminal data under the denoising strategy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_13506 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A monotone iterative reconstruction method for an inverse drift problem in a two-dimensional parabolic equation Zhang, Liuying Zhang, Wenlong Zhang, Zhidong Numerical Analysis We study an inverse drift problem for a two-dimensional parabolic equation on the unit square with mixed boundary conditions, where the drift coefficient is recovered from terminal observation data $g=u(\cdot,T)$. A monotone operator is constructed whose fixed point coincides with the unknown drift, yielding uniqueness in an admissible class and a constructive iterative reconstruction scheme. Numerical experiments illustrate the monotone convergence and the effectiveness of the proposed method, and show that it remains effective for noisy terminal data under the denoising strategy. |
| title | A monotone iterative reconstruction method for an inverse drift problem in a two-dimensional parabolic equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2604.13506 |