Uniqueness for an inverse coefficient problem of a weakly coupled parabolic system
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914543718891520 |
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| author | Ren, Caixuan Yu, Kai Li, Zhiyuan |
| author_facet | Ren, Caixuan Yu, Kai Li, Zhiyuan |
| contents | This paper considers the weakly coupled parabolic system $\partial_t u-\partial^2_xu +P(x)u=0$ with the homogeneous Neumann boundary condition, where \(P(x)\) is a \(2\times2\) symmetric real-valued function matrix. Under the assumption that the initial value \(a(x)\) is a generating element (i.e., it has a nonzero inner product with every eigenfunction), we prove that the coefficient matrix $ P(x)$ is uniquely determined by the boundary observation $u(0, t)$, $u(1, t)$, $0 < t < T$. The proof relies on the eigenfunction expansion of the solution to the initial-boundary value problem and an extension of the Gel'fand-Levitan theory to the parabolic system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07603 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniqueness for an inverse coefficient problem of a weakly coupled parabolic system Ren, Caixuan Yu, Kai Li, Zhiyuan Analysis of PDEs This paper considers the weakly coupled parabolic system $\partial_t u-\partial^2_xu +P(x)u=0$ with the homogeneous Neumann boundary condition, where \(P(x)\) is a \(2\times2\) symmetric real-valued function matrix. Under the assumption that the initial value \(a(x)\) is a generating element (i.e., it has a nonzero inner product with every eigenfunction), we prove that the coefficient matrix $ P(x)$ is uniquely determined by the boundary observation $u(0, t)$, $u(1, t)$, $0 < t < T$. The proof relies on the eigenfunction expansion of the solution to the initial-boundary value problem and an extension of the Gel'fand-Levitan theory to the parabolic system. |
| title | Uniqueness for an inverse coefficient problem of a weakly coupled parabolic system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.07603 |