Gauge symmetry and uniqueness in inverse problems for the JMGT equation

TL;DR

This paper proves the unique recovery of nonlinear and linear acoustic coefficients in the JMGT equation from boundary measurements on a Riemannian manifold, using linearization and geometric optics solutions.

Contribution

It demonstrates the first rigorous uniqueness results for the inverse boundary value problem for the JMGT equation, including gauge invariance considerations.

Findings

The nonlinear acoustic coefficient $eta$ is uniquely determined by boundary data.

Linear damping coefficients $ ext{ extalpha}$ and $q$ are recoverable up to gauge symmetry.

All coefficients are uniquely recoverable in a specific case.

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.