Xinchi Huang, Yavar Kian, É. Soccorsi, Masahiro Yamamoto
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Determination of source or initial values for acoustic equations with a time-fractional attenuation
We consider the inverse problem of determining the initial states or the source term of a hyperbolic equation damped by some non-local time-fractional derivative. This framework is relevant to medical imaging such as thermoacoustic or photoacoustic tomography. We prove a stability estimate for each of these two problems, with the aid of a Carleman estimate specifically designed for the governing equation.
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