Abstract:In this paper, we study an inverse boundary value problem for the Jordan--Moore--Gibson--Thompson equation on a simple Riemannian manifold. We consider an all boundary measurement map that maps Dirichlet boundary data and initial data to the corresponding Neumann-type boundary data and final-time data. Our main result shows that the nonlinear acoustic coefficient $\beta$ is uniquely determined by this measurement map, and the linear damping coefficients $\alpha$ and $q$, along with the internal source term $F$, can be recovered up to a gauge symmetry. As a corollary, we also establish a specific case in which all coefficients are uniquely recovered. The proof relies on the method of first-order and second-order linearization and on the construction of geometric optics solutions. In the intermediate step, we establish the unique recovery of the lower-order coefficients in the linearized MGT equation.
From: Dong Qiu [view email]
[v1]
Thu, 30 Apr 2026 15:42:01 UTC (24 KB)
[v2]
Wed, 27 May 2026 05:25:04 UTC (24 KB)
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