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 $(\partial_t-\Delta)^s+Q$ 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...
Gespeichert in:
| Hauptverfasser: | , , |
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| Dokumenttyp: | Article (Journal) Kapitel/Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
21 May 2019
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| In: |
Arxiv
Year: 2019, Pages: 1-34 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1905.08719
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| Verfasserangaben: | Ru-Yu Lai, Yi-Hsuan Lin, and Angkana Rüland |
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| 520 | |a In this article we study an inverse problem for the space-time fractional parabolic operator $(\partial_t-\Delta)^s+Q$ 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 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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