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


Lai, Ru-Yu; Lin, Yi-Hsuan; Rüland, Angkana (2020). The Calderón Problem for a Space-Time Fractional Parabolic Equation. SIAM Journal on Applied Mathematics, 52 (3), 2655-2688. DOI: 10.1137/19M1270288


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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

Open Access: Publication channel is not openly available

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


Abstract

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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Last updated on 2020-31-07 at 11:23