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In this paper, we consider the inverse problem of recovering a time-dependentnonlinearity for a third order nonlinear acoustic equation, which is known asthe Jordan-Moore-Gibson-Thompson equation (J-M-G-T equation for short). Thisthird order in time equation arises, for example, from the wave propagation inviscous thermally relaxing fluids. The well-posedness of the nonlinear equationis obtained for the small initial and boundary data. By the higher orderlinearization to the nonlinear equation, and construction of complex geometricoptics (CGO for short) solutions for the linearized equation, we derive theuniqueness of recovering the nonlinearity.

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