Regularity of solutions to time fractional diffusion equations

Binjie Li; Xiaoping Xie

doi:10.3934/dcdsb.2018340

Article Contents

2019, Volume 24, Issue 7: 3195-3210. Doi: 10.3934/dcdsb.2018340

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Regularity of solutions to time fractional diffusion equations

Binjie Li and
Xiaoping Xie^,

School of Mathematics, Sichuan University, Chengdu 610064, China

^* Corresponding author: Xiaoping Xie, xpxie@scu.edu.cn
^* Corresponding author: Xiaoping Xie, xpxie@scu.edu.cn

Received: May 31, 2017

Revised: November 30, 2017

Early access: January 2019

Published: May 2019

This work was supported by National Natural Science Foundation of China (11771312) and Major Research Plan of National Natural Science Foundation of China (91430105).

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Abstract

We derive some regularity estimates of the solution to a time fractional diffusion equation by using the Galerkin method. The regularity estimates partially unravel the singularity structure of the solution with respect to the time variable. We show that the regularity of the weak solution can be improved by subtracting some particular forms of singular functions.

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Mathematics Subject Classification: 26A33, 34A08, 35R11.

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