Gauge symmetry and uniqueness in inverse problems for the JMGT equation
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910262936731648 |
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| author | Qiu, Dong Xu, Xiang Ye, Yeqiong Zhou, Ting |
| author_facet | Qiu, Dong Xu, Xiang Ye, Yeqiong Zhou, Ting |
| contents | 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 $β$ is uniquely determined by this measurement map, and the linear damping coefficients $α$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_28023 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gauge symmetry and uniqueness in inverse problems for the JMGT equation Qiu, Dong Xu, Xiang Ye, Yeqiong Zhou, Ting Analysis of PDEs 35R30, 35L05 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 $β$ is uniquely determined by this measurement map, and the linear damping coefficients $α$ 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. |
| title | Gauge symmetry and uniqueness in inverse problems for the JMGT equation |
| topic | Analysis of PDEs 35R30, 35L05 |
| url | https://arxiv.org/abs/2604.28023 |