This research demonstrates stability in estimating a nonlinear coefficient in a third-order acoustic equation, indicating its dependence on boundary data.
In this paper, we study the stability in determining a time-dependent nonlinear coefficient appearing in the third-order in time Jordan-Moore-Gibson-Thompson equation of Westervelt type. By using the finite difference technique and constructing some geometric optics solutions to the linearized equation, together with the light-ray transform, a stability result of determining the time-dependent nonlinear term is obtained from the knowledge of the Neumann boundary data and only one terminal data.
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Fu et al. (2025) studied this question.
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