The Calderón Problem for the Fractional Wave Equation : Uniqueness and Optimal Stability
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
Published inSIAM Journal on Mathematical Analysis
© Authors, 2022
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
PublisherSociety for Industrial & Applied Mathematics (SIAM)
ISSN Search the Publication Forum0036-1410
Publication in research information system
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Additional information about fundingThe second author is partially supported by the Ministry of Science and Technology Taiwan, under the Columbus Program: MOST-109-2636-M-009-006, 2020-2025. The third author is partly supported by MOST 108-2115-M-002-002-MY3 and 109-2115-M-002-001-MY3.
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