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Stability estimates for the anisotropic wave equation from the Dirichlet-to-Neumann map

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  • In this article we seek stability estimates in the inverse problem of determining the potential or the velocity in a wave equation in an anisotropic medium from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the wave equation. We prove in dimension $n\geq 2$ that the knowledge of the Dirichlet-to-Neumann map for the wave equation uniquely determines the electric potential and we prove Hölder-type stability in determining the potential. We prove similar results for the determination of velocities close to 1.
    Mathematics Subject Classification: Primary: 58J32, 35L05; Secondary: 58J50.

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