We study the mathematical model of thermoacoustic tomography in media with a variable speed for a fixed time interval [0, T ] so that all signals issued from the domain leave it after time T . In the case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann series expansion. We give almost necessary and sufficient conditions for uniqueness and stability when the measurements are taken on a part of the boundary.
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Stefanov et al. (2009) studied this question.
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