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Inverse problems for advection diffusion equations in admissible geometries

ABSTRACT We study inverse boundary problems for the advection diffusion equation on an admissible manifold, i.e. a compact Riemannian manifold of dimension ≥3 with boundary, which is conformally embedded in a product of the Euclidean real line and a simple manifold. We prove the unique identifiability of the advection term of class and of class from the knowledge of the associated Dirichlet–to–Neumann map on the boundary of the manifold. This seems to be the first global identifiability result for possibly discontinuous advection terms.