Carleman estimates for the time-fractional advection-diffusion equations and applications. (5th March 2019)

• Record Type: Journal Article
• Authors: Huang, Xinchi; Li, Zhiyuan; Yamamoto, Masahiro
• Is Part Of: Inverse problems. Volume 35:Number 4(2019)
• Publication Date: 2019-03-05
• Subjects: time-fractional advection-diffusion equation -- Carleman estimate -- lateral Cauchy problem -- inverse source problem; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab0138
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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.