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

被引：0
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作者：
Songshu Liu
Lixin Feng
机构：
[1] Northeastern University at Qinhuangdao,School of Mathematics and Statistics
[2] Heilongjiang University,Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, School of Mathematical Sciences
来源：
Advances in Difference Equations | / 2018卷
关键词：
Inverse problem; Space-fractional diffusion equation; Optimal error bound; Modified kernel method; A posteriori parameter choice;
D O I：
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学科分类号：
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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