Well-posedness for a nonlocal nonlinear diffusion equation and applications to inverse problems

被引：2

作者：

Jing, Xiaohua ^{[1
]}

Jia, Junxiong ^{[1
]}

Peng, Jigen ^{[2
]}

机构：

[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian, Peoples R China

[2] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou, Peoples R China

来源：

APPLICABLE ANALYSIS | 2020年 / 99卷 / 15期

基金：

中国国家自然科学基金;

关键词：

Dinghua Xu; Determination of fractional order; inverse source problem; unique existence; nonlocal nonlinear diffusion equation; INTEGRODIFFERENTIAL EQUATIONS; WEAK SOLUTIONS; WAVE;

D O I：

10.1080/00036811.2019.1574342

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article investigates a space-time fractional diffusion equation with a nonlinear source and a space nonlocal operator. The well-posedness is demonstrated from using contraction mapping theorem and generalized Gronwall's inequality firstly. Based on the forward problem, we prove that a nonlinear source term and a fractional order of time derivative are uniquely determined by data which can be observed at one fixed spatial point.

引用

页码：2607 / 2621

页数：15

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