Inverse dynamic problem for the wave equation with periodic boundary conditions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910966548004864 |
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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 an interval $(0,2π)$ with periodic boundary conditions. We use a boundary triplet to set up the initial-boundary value problem. As an inverse data we use a response operator (dynamic Dirichlet-to-Neumann map). Using the auxiliary problem on the whole line, we derive equations of the inverse problem. We also establish the relationships between dynamic and spectral inverse data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18224 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse dynamic problem for the wave equation with periodic boundary conditions Mikhaylov, A. S. Mikhaylov, V. S. Analysis of PDEs Spectral Theory We consider the inverse dynamic problem for the wave equation with a potential on an interval $(0,2π)$ with periodic boundary conditions. We use a boundary triplet to set up the initial-boundary value problem. As an inverse data we use a response operator (dynamic Dirichlet-to-Neumann map). Using the auxiliary problem on the whole line, we derive equations of the inverse problem. We also establish the relationships between dynamic and spectral inverse data. |
| title | Inverse dynamic problem for the wave equation with periodic boundary conditions |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2505.18224 |