Journal
INVERSE PROBLEMS
Volume 35, Issue 4, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1361-6420/ab0138
Keywords
time-fractional advection-diffusion equation; Carleman estimate; lateral Cauchy problem; inverse source problem
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Funding
- JSPS [16H06712]
- National Natural Science Foundation of China [11801326]
- Japan Society for the Promotion of Science [15H05740]
- NSFC [11771270, 91730303]
- RUDN University Program 5-100
- A3 Foresight Program 'Modeling and Computation of Applied Inverse Problems' of Japan Society for the Promotion of Science
- Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University
- Grants-in-Aid for Scientific Research [16H06712] Funding Source: KAKEN
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In this article, we prove Carleman estimates for the generalized time-fractional advection-diffusion equations by considering the fractional derivative as perturbation for the first order time-derivative. As a direct application of the Carleman estimates, we show a conditional stability estimate for a lateral Cauchy problem for the time-fractional advection-diffusion equation, and we also investigate the stability of an inverse source problem.
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