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

Abstract

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.

References in corpus (4)

• Modified Szabo's wave equation models for lossy media obeying frequency power law
• Inverse Problems of Determining Sources of the Fractional Partial Differential Equations
• Theoretical stability and numerical reconstruction for an inverse source problem for hyperbolic equations
• Theoretical stability in coefficient inverse problems for general hyperbolic equations with numerical reconstruction