Gauge symmetry and uniqueness in inverse problems for the JMGT equation

Dong Qiu; Xiang Xu; Yeqiong Ye; Ting Zhou

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arXiv · 2604.28023

Gauge symmetry and uniqueness in inverse problems for the JMGT equation

Dong Qiu·Xiang Xu·Yeqiong Ye·Ting Zhou

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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.

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Dong Qiu, Xiang Xu, Yeqiong Ye, Ting Zhou. 2026-04-30. Gauge symmetry and uniqueness in inverse problems for the JMGT equation. https://arxiv.org/abs/2604.28023

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