A1 Journal article (refereed)
The Calderón Problem for the Fractional Wave Equation : Uniqueness and Optimal Stability (2022)
Kow, P.-Z., Lin, Y.-H., & Wang, J.-N. (2022). The Calderón Problem for the Fractional Wave Equation : Uniqueness and Optimal Stability. SIAM Journal on Mathematical Analysis, 54(3), 3379-3419. https://doi.org/10.1137/21M1444941
JYU authors or editors
Publication details
All authors or editors: Kow, Pu-Zhao; Lin, Yi-Hsuan; Wang, Jenn-Nan
Journal or series: SIAM Journal on Mathematical Analysis
ISSN: 0036-1410
eISSN: 1095-7154
Publication year: 2022
Volume: 54
Issue number: 3
Pages range: 3379-3419
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Publication country: United States
Publication language: English
DOI: https://doi.org/10.1137/21M1444941
Publication open access: Not open
Publication channel open access:
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/85312
Web address of parallel published publication (pre-print): https://arxiv.org/abs/2105.11324
Abstract
We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and stability estimate in the determination of the potential by the exterior Dirichlet-to-Neumann map. The main tools are the qualitative and quantitative unique continuation properties for the fractional Laplacian. For the stability, we also prove that the log type stability estimate is optimal. The log type estimate shows the striking difference between the inverse problems for the fractional and classical wave equations in the stability issue. The results hold for any spatial dimension n∈N
Keywords: partial differential equations; inverse problems
Free keywords: Calder´on problem; peridynamic; fractional Laplacian; nonlocal; fractional wave equation; strong uniqueness; Runge approximation; logarithmic stability
Contributing organizations
Ministry reporting: Yes
Reporting Year: 2022
JUFO rating: 2