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

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arxiv 2209.11157 v2 pith:AMIDHK4O submitted 2022-09-22 math.AP

Ching-Lung Lin , Yi-Hsuan Lin , Gunther Uhlmann This is my paper · ORCID
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keywords nonlocalparabolicproblemsinversecaldercauchycorrespondingdata
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Entanglement principle for the fractional Laplacian with applications to inverse problems

    math.AP 2024-12 conditional novelty 7.0 of 10

    A unique-continuation principle for sums of fractional Laplacians is proved on Euclidean space and applied to recover anisotropic coefficients and potentials in fractional polyharmonic equations.

  2. The Calder\'on problem for the logarithmic Schr\"odinger equation

    math.AP 2024-12 conditional novelty 6.0 of 10

    For the logarithmic Schrödinger operator, the Dirichlet-to-Neumann map uniquely determines bounded potentials in arbitrary space dimension, and monotonicity gives a constructive reconstruction.

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