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

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

2010-05-03

arxiv.org/abs/1005.0318v1

Mathematics

Analysis of PDEs

Scientific paper

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 H\"older-type stability in determining the potential.

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