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Stable determination of a vector field in a non-Self-Adjoint dynamical Schrödinger equation on Riemannian manifolds

  • * Corresponding author: Mourad Bellassoued

    * Corresponding author: Mourad Bellassoued 
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  • This paper deals with an inverse problem for a non-self-adjoint Schrödinger equation on a compact Riemannian manifold. Our goal is to stably determine a real vector field from the dynamical Dirichlet-to-Neumann map. We establish in dimension $ n\geq2 $, an Hölder type stability estimate for the inverse problem under study. The proof is mainly based on the reduction to an equivalent problem for an electro-magnetic Schrödinger equation and the use of a Carleman estimate designed for elliptic operators.

    Mathematics Subject Classification: Primary: 35R30; Secondary: 58J32.


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