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 with boundary of dimension $\ge 3$, 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 $H^1\cap L^\infty$ and of class $H^{2/3}\cap C^{0,1/3}$ 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.