The fractional anisotropic Calder\'{o}n problem for a nonlocal parabolic equation on closed Riemannian manifolds

Yi-Hsuan Lin

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arXiv · 2410.17750

The fractional anisotropic Calder\'{o}n problem for a nonlocal parabolic equation on closed Riemannian manifolds

Yi-Hsuan Lin

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Abstract

We consider the fractional anisotropic Calder\'on problem for the nonlocal parabolic equation $(\partial_t -\Delta_g)^s u=f$ ($0<s<1$) on closed Riemannian manifolds. More concretely, we can determine the Riemannian manifold $(M,g)$ up to isometry by using the local source-to-solution map in an arbitrarily small open cylinder in the spacetime domain. This can be regarded as a nonlocal analog of the anisotropic Calder\'on problem in the parabolic setting. We also study several useful properties for nonlocal parabolic operators by using comprehensive spectrum analysis with semigroup theory.

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Yi-Hsuan Lin. 2024-10-23. The fractional anisotropic Calder\'{o}n problem for a nonlocal parabolic equation on closed Riemannian manifolds. https://arxiv.org/abs/2410.17750

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