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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.00648 |
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| _version_ | 1866916014945468416 |
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| author | Bi, Minghui Gao, Yixian |
| author_facet | Bi, Minghui Gao, Yixian |
| contents | This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of the solution, \(Δu |_{\partial Ω}\) and \( \partial_{n}(Δu)|_{\partial Ω}.\) We first prove that the associated system operator generates a contraction semigroup, which ensures the well-posedness of the forward problem. A key observability inequality is then derived via multiplier techniques. Building on this foundation, explicit stability estimates for the inverse problem are obtained. These estimates demonstrate that the biharmonic structure inherently enhances the stability of parameter identification, with the stability constants exhibiting an explicit dependence on the damping coefficient via the factor \( (1 + γ)^{1/2} \). This work provides a rigorous theoretical basis for applications in non-destructive testing and dynamic inversion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00648 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lipschitz Stability for an Inverse Problem of Biharmonic Wave Equations with Damping Bi, Minghui Gao, Yixian Analysis of PDEs 37K55, 35Q30, 76D05 This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of the solution, \(Δu |_{\partial Ω}\) and \( \partial_{n}(Δu)|_{\partial Ω}.\) We first prove that the associated system operator generates a contraction semigroup, which ensures the well-posedness of the forward problem. A key observability inequality is then derived via multiplier techniques. Building on this foundation, explicit stability estimates for the inverse problem are obtained. These estimates demonstrate that the biharmonic structure inherently enhances the stability of parameter identification, with the stability constants exhibiting an explicit dependence on the damping coefficient via the factor \( (1 + γ)^{1/2} \). This work provides a rigorous theoretical basis for applications in non-destructive testing and dynamic inversion. |
| title | Lipschitz Stability for an Inverse Problem of Biharmonic Wave Equations with Damping |
| topic | Analysis of PDEs 37K55, 35Q30, 76D05 |
| url | https://arxiv.org/abs/2601.00648 |