English

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}
}