Reconstruction of potential and damping coefficients in a semi-linear wave equation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910102094610432 |
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| author | Bhardwaj, Rahul Kumar, Mandeep Vashisth, Manmohan |
| author_facet | Bhardwaj, Rahul Kumar, Mandeep Vashisth, Manmohan |
| contents | In this article, we investigate an inverse problem for a semi-linear wave equation posed on bounded domain in $\mathbb{R}^{n+1}$, with $n \geq 2$. Our primary objective is to reconstruct the damping coefficient, the linear and nonlinear potentials from the associated Dirichlet-to-Neumann map. The analysis is based on a \emph{higher-order linearization} method. As a key step, we establish the existence of suitable asymptotic solutions, crucial for reconstructing the nonlinear potential. In addition, we also provide a detailed study of the corresponding forward problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04822 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reconstruction of potential and damping coefficients in a semi-linear wave equation Bhardwaj, Rahul Kumar, Mandeep Vashisth, Manmohan Analysis of PDEs 35R30, 35L05, 44A12 In this article, we investigate an inverse problem for a semi-linear wave equation posed on bounded domain in $\mathbb{R}^{n+1}$, with $n \geq 2$. Our primary objective is to reconstruct the damping coefficient, the linear and nonlinear potentials from the associated Dirichlet-to-Neumann map. The analysis is based on a \emph{higher-order linearization} method. As a key step, we establish the existence of suitable asymptotic solutions, crucial for reconstructing the nonlinear potential. In addition, we also provide a detailed study of the corresponding forward problem. |
| title | Reconstruction of potential and damping coefficients in a semi-linear wave equation |
| topic | Analysis of PDEs 35R30, 35L05, 44A12 |
| url | https://arxiv.org/abs/2602.04822 |