# American Institute of Mathematical Sciences

November  2011, 5(4): 745-773. doi: 10.3934/ipi.2011.5.745

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

 1 University of Carthage, Department of Mathematics, Faculty of Sciences of Bizerte, 7021 Jarzouna Bizerte, Tunisia 2 Université Paris 13, CNRS, UMR 7539 LAGA, 99, avenue Jean-Baptiste Clément, F-93 430 Villetaneuse, France

Received  February 2011 Revised  September 2011 Published  November 2011

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.
Citation: Mourad Bellassoued, David Dos Santos Ferreira. Stability estimates for the anisotropic wave equation from the Dirichlet-to-Neumann map. Inverse Problems & Imaging, 2011, 5 (4) : 745-773. doi: 10.3934/ipi.2011.5.745
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