Optimal error bound and modified kernel method for a space-fractional backward diffusion problem

被引：3
|
作者：
Liu, Songshu [1 ]
Feng, Lixin [2 ]
机构：
[1] Northeastern Univ Qinhuangdao, Sch Math & Stat, Qinhuangdao, Peoples R China
[2] Heilongjiang Univ, Sch Math sci, Heilongjiang Prov Key Lab Theory & Computat Compl, Harbin, Heilongjiang, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2018年
基金：
美国国家科学基金会;
关键词：
Inverse problem; Space-fractional diffusion equation; Optimal error bound; Modified kernel method; A posteriori parameter choice; REGULARIZATION METHOD; CAUCHY-PROBLEM; EQUATION;
D O I：
10.1186/s13662-018-1728-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a backward problem for a space-fractional diffusion equation. This problem is ill-posed, i.e., the solution does not depend continuously on the data. The optimal error bound for the problem under a source condition is analyzed. Based on the idea of modified 'kernel', a regularization method is constructed, and the convergence estimates are obtained under a priori regularization parameter choice rule and a posteriori regularization parameter choice rule, respectively.
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页数：16
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