# Inverse problems for advection diffusion equations in admissible geometries

## TL;DR

This paper establishes the unique identifiability of advection terms in advection diffusion equations on certain geometric manifolds using boundary measurements, even when the advection terms are discontinuous.

## Contribution

It provides the first global identifiability result for possibly discontinuous advection terms in inverse boundary problems on admissible manifolds.

## Key findings

- Unique identifiability of advection term from boundary data
- Handles discontinuous advection terms in the analysis
- Applicable to manifolds conformally embedded in Euclidean-product spaces

## 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.