Recovery of a Source Term or a Speed with One Measurement and Applications
نویسنده
چکیده
We study the problem of recovery the source a.t;x/F.x/ in the wave equation in anisotropic medium with a known so that a.0;x/ 6D 0 with a single measurement. We use Carleman estimates combined with geometric arguments and give sharp conditions for uniqueness. We also study the non-linear problem of recovery the sound speed in the equation utt c .x/u D 0with one measurement. We give sharp conditions for stability, as well. An application to thermoacoustic tomography is also presented.
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