Existence and uniqueness of the weak solution of initial-boundary-value problems for the time-space fractional diffusion equation

被引：0

作者：

Wen, Yanhua ^{[1
]}

Xi, Xuanxuan ^{[1
]}

Wang, Jun ^{[1
]}

机构：

[1] Anhui Univ, Sch Math Sci, Hefei 230039, Anhui, Peoples R China

来源：

2017 32ND YOUTH ACADEMIC ANNUAL CONFERENCE OF CHINESE ASSOCIATION OF AUTOMATION (YAC) | 2017年

基金：

中国国家自然科学基金;

关键词：

Initial-boundary-value problem; Time-space fractional diffusion equation; Caputo fractional derivative; Existence and uniqueness; Maximum principle; LAPLACE OPERATOR;

D O I：

暂无

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper aims to study the existence and uniqueness of the weak solution of initial-boundary-value problems for the time-space fractional diffusion equation over a bounded domain Omega x [0, T], Omega subset of R-n. We first establish the existence of the weak solution of the initial-boundary-value problem for the time-space fractional diffusion equation and the proof is based on the eigenfunction expansion. Then to prove the uniqueness of the weak solution, a maximum principle for the time-space fractional diffusion equation is presented using the properties of the time fractional derivative and the fractional Laplace operator.

引用

页码：1053 / 1058

页数：6

共 19 条

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