Carleman estimates for the time-fractional advection-diffusion equations and applications
Analysis of PDEs
2019-04-15 v1
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 of a lateral Cauchy problem for the time-fractional advection-diffusion equation, and we also investigate the stability of an inverse source problem.
Keywords
Cite
@article{arxiv.1704.06011,
title = {Carleman estimates for the time-fractional advection-diffusion equations and applications},
author = {Zhiyuan Li and Xinchi Huang and Masahiro Yamamoto},
journal= {arXiv preprint arXiv:1704.06011},
year = {2019}
}