The Calderón problem for a space-time fractional parabolic equation

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. T...

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Bibliographic Details
Main Authors: Lai, Ru-Yu (Author) , Lin, Yi-Hsuan (Author) , Rüland, Angkana (Author)
Format: Article (Journal)
Language:English
Published: June 4, 2020
In: SIAM journal on mathematical analysis
Year: 2020, Volume: 52, Issue: 3, Pages: 2655-2688
ISSN:1095-7154
DOI:10.1137/19M1270288
Online Access:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1137/19M1270288
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Author Notes:Ru-Yu Lai, Yi-Hsuan Lin, and Angkana Rüland
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Summary: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.
Item Description:Gesehen am 27.08.2020
Physical Description:Online Resource
ISSN:1095-7154
DOI:10.1137/19M1270288