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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2503.18515 |
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| _version_ | 1866918291277086720 |
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| author | Blåsten, Emilia L. K. Helin, Tapio Kujanpää, Antti Oksanen, Lauri Railo, Jesse |
| author_facet | Blåsten, Emilia L. K. Helin, Tapio Kujanpää, Antti Oksanen, Lauri Railo, Jesse |
| contents | We consider the following inverse problem: Suppose a $(1+1)$-dimensional wave equation on $\mathbb{R}_+$ with zero initial conditions is excited with a Neumann boundary data modelled as a white noise process. Given also the Dirichlet data at the same point, determine the unknown first order coefficient function of the system.
We first establish that direct problem is well-posed. The inverse problem is then solved by showing that correlations of the boundary data determine the Neumann-to-Dirichlet operator in the sense of distributions, which is known to uniquely identify the coefficient. This approach has applications in acoustic measurements of internal cross-sections of fluid pipes such as pressurised water supply pipes and vocal tract shape determination. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18515 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Recovering a (1+1)-dimensional wave equation from a single white noise boundary measurement Blåsten, Emilia L. K. Helin, Tapio Kujanpää, Antti Oksanen, Lauri Railo, Jesse Analysis of PDEs Statistics Theory 35R30, 60H30 We consider the following inverse problem: Suppose a $(1+1)$-dimensional wave equation on $\mathbb{R}_+$ with zero initial conditions is excited with a Neumann boundary data modelled as a white noise process. Given also the Dirichlet data at the same point, determine the unknown first order coefficient function of the system. We first establish that direct problem is well-posed. The inverse problem is then solved by showing that correlations of the boundary data determine the Neumann-to-Dirichlet operator in the sense of distributions, which is known to uniquely identify the coefficient. This approach has applications in acoustic measurements of internal cross-sections of fluid pipes such as pressurised water supply pipes and vocal tract shape determination. |
| title | Recovering a (1+1)-dimensional wave equation from a single white noise boundary measurement |
| topic | Analysis of PDEs Statistics Theory 35R30, 60H30 |
| url | https://arxiv.org/abs/2503.18515 |