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Article Dans Une Revue Analysis and Applications Année : 2023

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

Résumé

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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Dates et versions

hal-04396901 , version 1 (16-01-2024)

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Xinchi Huang, Yavar Kian, Éric Soccorsi, Masahiro Yamamoto. Determination of source or initial values for acoustic equations with a time-fractional attenuation. Analysis and Applications, 2023, 21 (05), pp.1105-1130. ⟨10.1142/S0219530523500100⟩. ⟨hal-04396901⟩
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