On an inverse dynamic problem for the wave equation with a potential on a real line
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918146118516736 |
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| author | Mikhaylov, A. S. Mikhaylov, V. S. |
| author_facet | Mikhaylov, A. S. Mikhaylov, V. S. |
| contents | We consider the inverse dynamic problem for the wave equation with a potential on a real line. The forward initial-boundary value problem is set up with a help of boundary triplets. As an inverse data we use an analog of a response operator (dynamic Dirichlet-to-Neumann map). We derive equations of inverse problem and also point out the relationship between dynamic inverse problem and spectral inverse problem from a matrix-valued measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17668 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On an inverse dynamic problem for the wave equation with a potential on a real line Mikhaylov, A. S. Mikhaylov, V. S. Analysis of PDEs We consider the inverse dynamic problem for the wave equation with a potential on a real line. The forward initial-boundary value problem is set up with a help of boundary triplets. As an inverse data we use an analog of a response operator (dynamic Dirichlet-to-Neumann map). We derive equations of inverse problem and also point out the relationship between dynamic inverse problem and spectral inverse problem from a matrix-valued measure. |
| title | On an inverse dynamic problem for the wave equation with a potential on a real line |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.17668 |