Carleman estimates for the time-fractional advection-diffusion equations and applications. (5th March 2019) - Huang, Xinchi; Li, Zhiyuan; Yamamoto, Masahiro
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.