Inverse boundary value problem for the Convection-Diffusion equation with local data

We study a local data inverse problem for the time-dependent Convection-Diffusion Equation (CDE) in a bounded domain where a part of the boundary is treated to be inaccessible. Up on assuming the inaccessible part to be flat, we seek for the unique determination of the time-dependent convection and the density terms from the knowledge of the boundary data measured outside the inaccessible part. In the process, we show that there is a natural gauge in the perturbations, and we prove that this is the only obstruction in the uniqueness result.