Ibtissem BEN AICHA – Groupe de Travail Guide d’ondes, milieux stratifiés et problèmes inverses (TBA)

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Date(s) - 17 juin 2015

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Title :Stability estimate for hyperbolic inverse problem with time dependentcoefficient We study the stability in the inverse problem of determining the time dependentzeroth-order coefficient q(t, x) arising in the wave equation, from boundary observations.We derive, in dimension n>3 , a log-type stability estimate in the determinationof q from the Dirichlet-to-Neumann map, in a subset of our domain assuming that itis known outside this subset. Moreover, we prove that we can extend this result to thedetermination of q in a larger region, and then in the whole domain provided that wehave much more data.[