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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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
June 4, 2020
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| 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 |
| 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. |
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| Item Description: | Gesehen am 27.08.2020 |
| Physical Description: | Online Resource |
| ISSN: | 1095-7154 |
| DOI: | 10.1137/19M1270288 |