We consider an inverse problem of recovering the damping coefficient and initial condition for a wave equation through a single boundary measurement. The problem is motivated from photoacoustic and thermoacoustic tomography when attenuation is presented in the models. Through a proper decomposition, we convert the problem into a standard inverse hyperbolic problem, and we establish a Lipschitz stability estimate through Carleman estimates.
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Shitao Liu (2025) studied this question.
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