Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2510.02553 |
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Sommario:
- 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.