Entanglement principle and fractional Calderón problem for nonlocal parabolic operators

Abstract

We examine inverse problems for the variable-coefficient nonlocal parabolic operator $({\partial }_t-{\Delta }_g{)}^s$, where $0<s<1$. This article makes two primary contributions. First, we introduce a novel entanglement principle for these operators under suitable smoothness conditions. Second, we prove that lower-order perturbations can be uniquely determined from the associated Dirichlet-to-Neumann map using this principle. However, due to insufficient solution regularity, direct application of the entanglement principle to the inverse problem is not feasible. To address this, we derive a modified entanglement principle, enabling the effective resolution of related inverse problems.

24 pages