Stability in Inverse Problem for a Moore–Gibson–Thompson Equation with Time-Dependent Coefficient

In this paper, we consider the inverse problem of determining a time-dependent variable “damping” coefficient depending on a viscosity of the fluid appearing in the Moore–Gibson–Thompson equation. This equation arises, e.g., as a linearization of a model that describes the ultrasound wave propagation in viscous thermally relaxing fluids, and displays a variety of dynamical behaviors. For the inverse problem considered in this work, with all the initial data involved, we obtain a stability result of recovering the time-dependent viscosity by means of geometric optics solutions, and the property of some integral transforms.