A1 Journal article (refereed)
The Calderón Problem for a Space-Time Fractional Parabolic Equation (2020)

Lai, R.-Y., Lin, Y.-H., & Rüland, A. (2020). The Calderón Problem for a Space-Time Fractional Parabolic Equation. SIAM Journal on Applied Mathematics, 52(3), 2655-2688. https://doi.org/10.1137/19M1270288

JYU authors or editors

Publication details

All authors or editors: Lai, Ru-Yu; Lin, Yi-Hsuan; Rüland, Angkana

Journal or series: SIAM Journal on Applied Mathematics

ISSN: 1095-712X

eISSN: 0036-1399

Publication year: 2020

Volume: 52

Issue number: 3

Pages range: 2655-2688

Publisher: Society for Industrial and Applied Mathematics

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1137/19M1270288

Publication open access: Not open

Publication channel open access:

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1905.08719


In this article we study an inverse problem for the space-time fractional parabolic operator (partial derivative(t) -Delta)(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 new Carleman estimate for the associated degenerate parabolic Caffarelli- Silvestre extension. Furthermore, we also discuss constructive single measurement results based on the approximation and unique continuation properties of the equation.

Keywords: inverse problems; partial differential equations

Free keywords: nonlocal; fractional parabolic Calderon problem; unique continuation property; Runge approximation; Carleman estimate; degenerate parabolic equations

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Related projects

Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 3

Last updated on 2021-07-07 at 21:35