Simultaneous determination of wave speed, diffusivity and nonlinearity in the Westervelt equation using complex time-periodic solutions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908537696813056 |
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| author | Acosta, Sebastian Palacios, Benjamin |
| author_facet | Acosta, Sebastian Palacios, Benjamin |
| contents | We consider an inverse problem governed by the Westervelt equation with linear diffusivity and quadratic-type nonlinearity. The objective of this problem is to recover all the coefficients of this nonlinear partial differential equation. We show that, by constructing complex-valued time-periodic solutions excited from the boundary time-harmonically at a sufficiently high frequency, knowledge of the first- and second-harmonic Cauchy data at the boundary is sufficient to simultaneously determine the wave speed, diffusivity and nonlinearity in the interior of the domain of interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10718 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simultaneous determination of wave speed, diffusivity and nonlinearity in the Westervelt equation using complex time-periodic solutions Acosta, Sebastian Palacios, Benjamin Analysis of PDEs Medical Physics 35R30, 35L05, 92C55, 35G20 We consider an inverse problem governed by the Westervelt equation with linear diffusivity and quadratic-type nonlinearity. The objective of this problem is to recover all the coefficients of this nonlinear partial differential equation. We show that, by constructing complex-valued time-periodic solutions excited from the boundary time-harmonically at a sufficiently high frequency, knowledge of the first- and second-harmonic Cauchy data at the boundary is sufficient to simultaneously determine the wave speed, diffusivity and nonlinearity in the interior of the domain of interest. |
| title | Simultaneous determination of wave speed, diffusivity and nonlinearity in the Westervelt equation using complex time-periodic solutions |
| topic | Analysis of PDEs Medical Physics 35R30, 35L05, 92C55, 35G20 |
| url | https://arxiv.org/abs/2509.10718 |