Inverse problem of recovering a time-dependent nonlinearity appearing in third-order nonlinear acoustic equations

Abstract

In this paper, we consider the inverse problem of recovering a time-dependent nonlinearity for a third order nonlinear acoustic equation, which is known as the Jordan-Moore-Gibson-Thompson equation (J-M-G-T equation for short). This third order in time equation arises, for example, from the wave propagation in viscous thermally relaxing fluids. The well-posedness of the nonlinear equation is obtained for the small initial and boundary data. By the higher order linearization to the nonlinear equation, and construction of complex geometric optics (CGO for short) solutions for the linearized equation, we derive the uniqueness of recovering the nonlinearity.