A modified regularized algorithm for a semilinear space-fractional backward diffusion problem

被引：1
|
作者：
Jiang, Xiaoying [1 ]
Xu, Dinghua [1 ,2 ]
Zhang, Qifeng [1 ]
机构：
[1] Zhejiang Sci Tech Univ, Dept Math, Coll Sci, Hangzhou 310018, Zhejiang, Peoples R China
[2] Shanghai Univ Finance & Econ, Sch Math, Shanghai 200433, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2017年 / 40卷 / 16期
基金：
中国国家自然科学基金;
关键词：
backward diffusion problem; space-fractional equations; modified regularization; variational adjoint method; INVERSE PROBLEM; HEAT;
D O I：
10.1002/mma.4449
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate a backward problem for a space-fractional partial differential equation. The main purpose is to propose a modified regularization method for the inverse problem. The existence and the uniqueness for the modified regularized solution are proved. To derive the gradient of the optimization functional, the variational adjoint method is introduced, and hence, the unknown initial value is reconstructed. Finally, numerical examples are provided to show the effectiveness of the proposed algorithm. Copyright (C) 2017 John Wiley & Sons, Ltd.
引用
收藏
页码：5996 / 6006
页数：11
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