Abstract
This paper is devoted to the reconstruction of the time and space-dependent coefficient in an inverse hyperbolic problem in a bounded domain. Using a local Carleman estimate we prove the uniqueness and a Hölder stability in the determination of the conductivity by a single measurement on the lateral boundary. Our numerical examples show possibility of the determination of the location and the large contrast of the space-dependent function in three dimensions.
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Acknowledgments
The part of the research was done during the sabbatical stay of LB at the Institut de Mathématiques de Marseille, Aix-Marseille University, France, which was supported by the sabbatical programme at the Faculty of Science, University of Gothenburg, Sweden.
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Beilina, L., Cristofol, M., Li, S. (2018). Uniqueness, Stability and Numerical Reconstruction of a Time and Space-Dependent Conductivity for an Inverse Hyperbolic Problem. In: Beilina, L., Smirnov, Y. (eds) Nonlinear and Inverse Problems in Electromagnetics. PIERS PIERS 2017 2017. Springer Proceedings in Mathematics & Statistics, vol 243. Springer, Cham. https://doi.org/10.1007/978-3-319-94060-1_10
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