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Stability estimate for an inverse problem for the wave equation in a magnetic field
Authors:Mourad Bellassoued  Hajer Benjoud
Institution:1. Faculty of Sciences of Bizerte, Department of Mathematics , 7021 Jarzouna Bizerte, Tunisia mourad.bellassoued@fsb.rnu.tn;3. Faculty of Sciences of Bizerte, Department of Mathematics , 7021 Jarzouna Bizerte, Tunisia
Abstract:In this article, we prove stability estimate of the inverse problem of determining the magnetic field entering the magnetic wave equation in a bounded smooth domain in ? d from boundary observations. This information is enclosed in the hyperbolic (dynamic) Dirichlet-to-Neumann map associated to the solutions to the magnetic wave equation. We prove in dimension d ≥ 2 that the knowledge of the Dirichlet-to-Neumann map for the magnetic wave equation measured on the boundary determines uniquely the magnetic field and we prove a Hölder-type stability in determining the magnetic field induced by the magnetic potential.
Keywords:stability estimate  hyperbolic inverse problem  magnetic field  Dirichlet-to-Neumann-map
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