In this article we study an inverse problem for the space-time fractional parabolic operator (∂t - Δ)s + Q with 0 < s < 1 in any space dimension. We uniquely determine the unknown bounded potential Q from infinitely many exterior Dirichlet-to-Neumann type measurements. This relies on Runge approximation and the dual global weak unique continuation properties of the equation under consideration. In discussing weak unique continuation of our operator, a main feature of our argument relies on a new Carleman estimate for the associated degenerate parabolic Caffarelli- Silvestre extension. Furthermore, we also discuss constructive single measurement results based on the approximation and unique continuation properties of the equation.
- Carleman estimate
- Degenerate parabolic equations
- Fractional parabolic Calderón problem
- Runge approximation
- Unique continuation property