Optimal error bound and truncation regularization method for a backward time-fractional diffusion problem in Hilbert scales

被引：7
|
作者：
Dinh Nguyen Duy Hai [1 ,2 ]
Dang Duc Trong [3 ]
机构：
[1] Duy Tan Univ, Inst Fundamental & Appl Sci, Ho Chi Minh City 700000, Vietnam
[2] Duy Tan Univ, Fac Nat Sci, Da Nang 550000, Vietnam
[3] Viet Nam Natl Univ, Univ Nat Sci, Dept Math & Comp Sci, Ho Chi Minh City, Vietnam
来源：
APPLIED MATHEMATICS LETTERS | 2020年 / 107卷
关键词：
Backward time-fractional diffusion equation; Ill-posedness; Truncation method; Optimal estimates; EQUATIONS;
D O I：
10.1016/j.aml.2020.106448
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 time-fractional diffusion equation in a general abstract Hilbert space. We show that the problem is ill-posed and further apply a truncation regularization method to solve it. Based on a Holder-type smoothness assumption of the exact solution, asymptotically optimal estimates for the worst case error of the method in Hilbert scales are proved. (C) 2020 Elsevier Ltd. All rights reserved.
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页数：9
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