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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.02553 |
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| _version_ | 1866908574281629696 |
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| author | Wendels, Mike |
| author_facet | Wendels, Mike |
| contents | The Westervelt equation models the propagation of nonlinear acoustic waves in a regime well-suited for applications such as medical ultrasound imaging. In this work, we prove that the nonlinear parameter, as well as the sound speed, can be stably recovered from the Dirichlet-to-Neumann map associated with the non-diffusive Westervelt equation in (1+3)-dimensions. This result is essential for the feasibility of reconstruction methods. The Dirichlet-to-Neumann map encodes boundary measurements by associating a prescribed pressure profile on the boundary with the resulting pressure fluctuations. We prove stability provided the sound speed is a priori known to be close to a reference sound speed and under certain geometrical conditions. We also verify the result through numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02553 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable determination of the nonlinear parameter in the non-diffusive Westervelt equation from the Dirichlet-to-Neumann map Wendels, Mike Analysis of PDEs The Westervelt equation models the propagation of nonlinear acoustic waves in a regime well-suited for applications such as medical ultrasound imaging. In this work, we prove that the nonlinear parameter, as well as the sound speed, can be stably recovered from the Dirichlet-to-Neumann map associated with the non-diffusive Westervelt equation in (1+3)-dimensions. This result is essential for the feasibility of reconstruction methods. The Dirichlet-to-Neumann map encodes boundary measurements by associating a prescribed pressure profile on the boundary with the resulting pressure fluctuations. We prove stability provided the sound speed is a priori known to be close to a reference sound speed and under certain geometrical conditions. We also verify the result through numerical experiments. |
| title | Stable determination of the nonlinear parameter in the non-diffusive Westervelt equation from the Dirichlet-to-Neumann map |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.02553 |