Carleman estimates for the time-fractional advection-diffusion equations and applications

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. © 2019 IOP Publishing Ltd.

Authors
Huang X.1 , Li Z.3 , Yamamoto M. 1, 2
Journal
Inverse Problems
Publisher
Institute of Physics Publishing
Number of issue
4
Language
English
Status
Published
Link
External link
DOI
10.1088/1361-6420/ab0138
Number
045003
Volume
35
Year
2019
Organizations
  • 1 Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
  • 2 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
  • 3 School of Mathematics and Statistics, Shandong University of Technology, Zibo, Shandong, 255049, China
Keywords
Carleman estimate; Inverse source problem; Lateral Cauchy problem; Time-fractional advection-diffusion equation
Date of creation
19.07.2019
Date of change
19.07.2019
Short link
https://repository.rudn.ru/en/records/article/record/38721/
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