Stability estimate for a hyperbolic inverse problem with time-dependent coefficient. (18th November 2015) - Aïcha, Ibtissem Ben
Abstract: We study the stability issue in the inverse problem of determining the time-dependent coefficient of order zero appearing in the wave equation, from boundary observations. In dimension we derive a log-type stability estimate with respect to the Dirichlet-to-Neumann map for the restriction of q to a suitable subset of the domain. This is provided q is known outside the above subset. Moreover, by enlarging the set of data, we prove that q can be stably retrieved in larger subsets of the domain, including the whole domain itself.