Stable determination of a time-dependent matrix potential for a wave equation in an infinite waveguide
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912013506052096 |
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| author | Kumar, Nitesh Sarkar, Tanmay Vashisth, Manmohan |
| author_facet | Kumar, Nitesh Sarkar, Tanmay Vashisth, Manmohan |
| contents | We analyze the stability of an inverse problem for determining the time-dependent matrix potential appearing in the Dirichlet initial-boundary value problem for the wave equation in an unbounded cylindrical waveguide. The observation is given by the input-output map associated with the wave equation. Considering a suitable geometric optics solution and with the help of light ray transform, we demonstrate the stability estimate in the determination of the time-dependent matrix potential from the given input-output map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01913 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stable determination of a time-dependent matrix potential for a wave equation in an infinite waveguide Kumar, Nitesh Sarkar, Tanmay Vashisth, Manmohan Analysis of PDEs 35R30, 35L05 We analyze the stability of an inverse problem for determining the time-dependent matrix potential appearing in the Dirichlet initial-boundary value problem for the wave equation in an unbounded cylindrical waveguide. The observation is given by the input-output map associated with the wave equation. Considering a suitable geometric optics solution and with the help of light ray transform, we demonstrate the stability estimate in the determination of the time-dependent matrix potential from the given input-output map. |
| title | Stable determination of a time-dependent matrix potential for a wave equation in an infinite waveguide |
| topic | Analysis of PDEs 35R30, 35L05 |
| url | https://arxiv.org/abs/2409.01913 |