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Determination of source or initial values for acoustic equations with a time-fractional attenuation

Analysis and Applications, ISSN: 1793-6861, Vol: 21, Issue: 5, Page: 1105-1130
2023
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Article Description

In this paper, we consider the inverse problems 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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