The Calderón problem for nonlocal parabolic operators

2022/09/22 by Lin, Ching-Lung, Lin, Yi-Hsuan, Uhlmann, Gunther · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.11157

Abstract

We investigate inverse problems in the determination of leading coefficients for nonlocal parabolic operators, by knowing the corresponding Cauchy data in the exterior space-time domain. The key contribution is that we reduce nonlocal parabolic inverse problems to the corresponding local inverse problems with the lateral boundary Cauchy data. In addition, we derive a new equation and offer a novel proof of the unique continuation property for this new equation. We also build both uniqueness and non-uniqueness results for both nonlocal isotropic and anisotropic parabolic Calderón problems, respectively.

Cited by

• Entanglement principle and fractional Calderón problem for nonlocal parabolic operators

Related

• The Calderón problem for nonlocal parabolic operators: A new reduction from the nonlocal to the local
• The Calderón problem for a nonlocal diffusion equation with time-dependent coefficients
• The Calderón problem for nonlocal operators
• The Calderón problem for space-time fractional parabolic operators with variable coefficients
• Boundary Control and Calderón type Inverse Problems in Non-local heat equation