The Calderón Problem for the Fractional Wave Equation : Uniqueness and Optimal Stability
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
Main Authors
Format
Articles
Research article
Published
2022
Series
Subjects
Publication in research information system
Publisher
Society for Industrial & Applied Mathematics (SIAM)
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202302021594Use this for linking
Review status
Peer reviewed
ISSN
0036-1410
DOI
https://doi.org/10.1137/21M1444941
Language
English
Published in
SIAM Journal on Mathematical Analysis
Citation
- 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
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Additional information about funding
The 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.
Copyright© Authors, 2022