Linearized Boundary Control Method for Damping Reconstruction in an Acoustic Inverse Boundary Value Problem
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915849017753600 |
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| author | Yang, Tianyu Yang, Yang |
| author_facet | Yang, Tianyu Yang, Yang |
| contents | We develop a linearized boundary control method for the inverse boundary value problem of determining the damping coefficient in the damped wave equation. The objective is to reconstruct an unknown perturbation in a known background damping from the linearized Neumann-to-Dirichlet map. When the linearization is at a constant background damping, we derive a reconstructive algorithm with stability estimates based on the boundary control method in dimension $n\geq 1$. The reconstruction algorithm is implemented in one dimension to validate its numerical feasibility. When the linearization is at a non-constant background damping, we establish an increasing stability estimate in the time domain in dimension $n\geq 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08888 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Linearized Boundary Control Method for Damping Reconstruction in an Acoustic Inverse Boundary Value Problem Yang, Tianyu Yang, Yang Analysis of PDEs 35R30, 35L05 We develop a linearized boundary control method for the inverse boundary value problem of determining the damping coefficient in the damped wave equation. The objective is to reconstruct an unknown perturbation in a known background damping from the linearized Neumann-to-Dirichlet map. When the linearization is at a constant background damping, we derive a reconstructive algorithm with stability estimates based on the boundary control method in dimension $n\geq 1$. The reconstruction algorithm is implemented in one dimension to validate its numerical feasibility. When the linearization is at a non-constant background damping, we establish an increasing stability estimate in the time domain in dimension $n\geq 3$. |
| title | Linearized Boundary Control Method for Damping Reconstruction in an Acoustic Inverse Boundary Value Problem |
| topic | Analysis of PDEs 35R30, 35L05 |
| url | https://arxiv.org/abs/2603.08888 |