Mourad Bellassoued – Stability estimates for the anisotropic wave and Schrödinger equations from the Dirichlet to Neumann map

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Date(s) - 23 juin 2010

Catégories Pas de Catégories

In this talk, we want to obtain stability estimates for the inverse problem of determining the electric potential or the conformal factor in a wave or Schrodinger equations in an anisotropic media with Dirichlet data 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 measured on the boundary uniquely determines the electric potential and we prove Hölder-type stability in determining the potential. We prove similar results for the determination of a conformal factor close to $.