Conditional stability for an inverse problem of a fully-discrete stochastic hyperbolic equation
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910210319187968 |
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| author | Wu, Bin Zhu, Xu Zhou, Wenwen Wang, Zewen |
| author_facet | Wu, Bin Zhu, Xu Zhou, Wenwen Wang, Zewen |
| contents | In this paper, we investigate a discrete inverse problem of determining three unknowns, i.e. initial displacement, initial velocity and random source term, in a fully discrete approximation of one-dimensional stochastic hyperbolic equation. We firstly prove a new Carleman estimate for the fully-discrete stochastic hyperbolic equation. Based on this Carleman estimate, we then establish a Lipschitz stability for this discrete inverse problem by the discrete spatial derivative data at the left endpoint and the measurements of the solution and its time derivative at the final time. Owing to the discrete setting, an extra term with respect to mesh size arises in the right-hand side of the stability estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07072 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conditional stability for an inverse problem of a fully-discrete stochastic hyperbolic equation Wu, Bin Zhu, Xu Zhou, Wenwen Wang, Zewen Analysis of PDEs In this paper, we investigate a discrete inverse problem of determining three unknowns, i.e. initial displacement, initial velocity and random source term, in a fully discrete approximation of one-dimensional stochastic hyperbolic equation. We firstly prove a new Carleman estimate for the fully-discrete stochastic hyperbolic equation. Based on this Carleman estimate, we then establish a Lipschitz stability for this discrete inverse problem by the discrete spatial derivative data at the left endpoint and the measurements of the solution and its time derivative at the final time. Owing to the discrete setting, an extra term with respect to mesh size arises in the right-hand side of the stability estimate. |
| title | Conditional stability for an inverse problem of a fully-discrete stochastic hyperbolic equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.07072 |