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arXiv · 1905.08719

The Calderón problem for a space-time fractional parabolic equation

Ru-Yu Lai·Yi-Hsuan Lin·Angkana Rüland
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Abstract

In this article we study an inverse problem for the space-time fractional parabolic operator $(\partial_t-Δ)^s+Q$ with $0<s<1$ in any space dimension. We uniquely determine the unknown bounded potential $Q$ from infinitely many exterior Dirichlet-to-Neumann type measurements. This relies on Runge approximation and the dual global weak unique continuation properties of the equation under consideration. In discussing weak unique continuation of our operator, a main feature of our argument relies on a Carleman estimate for the associated fractional parabolic Caffarelli-Silvestre extension. Furthermore, we also discuss constructive single measurement results based on the approximation and unique continuation properties of the equation.

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Ru-Yu Lai, Yi-Hsuan Lin, Angkana Rüland. 2019-05-21. The Calderón problem for a space-time fractional parabolic equation. https://arxiv.org/abs/1905.08719

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