Carleman estimates for second-order hyperbolic systems in anisotropic cases and applications

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Date(s) - 13/07/2016
15 h 00 min - 16 h 00 min


We consider Carleman-type estimate for second order hyperbolic systems in an anisotropic case and its applications. We first establish a Carleman-type estimate for hyperbolic systems in which the coefficient matrices satisfy suitable conditions. Then we apply this Carleman estimate to an inverse source problem for second-order hyperbolic systems in an anisotropic case and prove an estimate of the Hölder type. We further apply this Carleman estimate to an inverse coefficient problem for Maxwell’s equations in a uniaxially anisotropic medium, and prove a stability estimate of Lipschitz type, provided that unknown coefficients satisfy some a priori conditions.

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