Unique continuation principle for the one-dimensional time-fractional diffusion equation

Zhiyuan Li; Masahiro Yamamoto

Unique continuation principle for the one-dimensional time-fractional diffusion equation

Analysis of PDEs 2018-06-19 v1

Authors: Zhiyuan Li , Masahiro Yamamoto

Abstract

This paper deals with the unique continuation of solutions for a one-dimensional anomalous diffusion equation with Caputo derivative of order $\alpha\in(0,1)$ . Firstly, the uniqueness of solutions to a lateral Cauchy problem for the anomalous diffusion equation is given via the Theta function method, from which we further verify the unique continuation principle.

Keywords

fractional differential equations fractional diffusion equations nonlinear diffusion equations

Cite

@article{arxiv.1806.06164,
  title  = {Unique continuation principle for the one-dimensional time-fractional diffusion equation},
  author = {Zhiyuan Li and Masahiro Yamamoto},
  journal= {arXiv preprint arXiv:1806.06164},
  year   = {2018}
}

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