Rohit Kumar MishraAnamika PurohitManmohan Vashisth2025-12-292025-12-292025-12-0110.1007/s40687-025-00556-02-s2.0-105017011462http://repository.iitgn.ac.in/handle/IITG2025/33735We consider a partial data inverse problem for a time-dependent convection–diffusion equation on an admissible manifold. We prove that the time-dependent convection term and time-dependent density can be recovered uniquely modulo a known gauge invariance. There have been several works on inverse problems related to the steady-state convection–diffusion operator in Euclidean as well as in Riemannian geometry settings; however, inverse problems related to time-dependent convection–diffusion equation on a manifold are not studied in the prior works, which is the main aim of this paper. In fact, to the best of our knowledge, the problem studied here is the first work related to a partial data inverse problem for recovering both first- and zeroth-order time-dependent perturbations of evolution equations in the Riemannian geometry setting.falseInverse problemsTime-dependent coefficientsConvection–diffusion equationPartial boundary dataAdmissible manifoldCarleman estimatesGeometric optics solutionsAdmissible manifold | Carleman estimates | Convection–diffusion equation | Geometric optics solutions | Inverse problems | Partial boundary data | Time-dependent coefficientsArticle21979847December 2025075arArticle0WOS:001577825200001