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arXiv · 2205.12509

The Calder\'on problem for space-time fractional parabolic operators with variable coefficients

Agnid Banerjee·Soumen Senapati
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Abstract

We study an inverse problem for variable coefficient fractional parabolic operators of the form $(\partial_t -\operatorname{div}(A(x) \nabla_x)^s + q(x,t)$ for $s\in(0,1)$ and show the unique recovery of $q$ from exterior measured data. Similar to the fractional elliptic case, we use Runge type approximation argument which is obtained via a global weak unique continuation property. The proof of such a unique continuation result involves a new Carleman estimate for the associated variable coefficient extension operator. In the latter part of the work, we prove analogous unique determination results for fractional parabolic operators with drift.

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Agnid Banerjee, Soumen Senapati. 2022-05-25. The Calder\'on problem for space-time fractional parabolic operators with variable coefficients. https://arxiv.org/abs/2205.12509

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