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

2018/06/16 by Zhiyuan Li, Masahiro Yamamoto, Li, Zhiyuan +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1806.06164

arxiv created 2018/06/16 · arxiv updated 2018/06/19

Abstract

This paper deals with the unique continuation of solutions for a one-dimensional anomalous diffusion equation with Caputo derivative of order α∈(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.

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