The Calder\'{o}n problem for nonlocal parabolic operators

Ching-Lung Lin; Yi-Hsuan Lin; Gunther Uhlmann

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arXiv · 2209.11157

The Calder\'{o}n problem for nonlocal parabolic operators

Ching-Lung Lin·Yi-Hsuan Lin·Gunther Uhlmann

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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 Calder\'on problems, respectively.

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Ching-Lung Lin, Yi-Hsuan Lin, Gunther Uhlmann. 2022-09-22. The Calder\'{o}n problem for nonlocal parabolic operators. https://arxiv.org/abs/2209.11157

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