A Riesz–Feller space‐fractional backward diffusion problem with a time‐dependent coefficient: regularization and error estimates

In this paper, we consider a Riesz–Feller space‐fractional backward diffusion problem with a time‐dependent coefficient ut(x,t)=ℓ(t)xDθγu(x,t)+f(x,t),(x,t)∈R×(0,T). We show that this problem is ill‐posed; therefore, we propose a convolution regularization method to solve it. New error estimates for...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2017-07, Vol.40 (11), p.4040-4064
Main Authors: Tuan, Nguyen Huy, Trong, Dang Duc, Hai, Dinh Nguyen Duy, Thanh, Duong Dang Xuan
Format: Article
Language:English
Subjects:
Coefficients
Convolution
error estimate
Errors
Estimates
Ill posed problems
ill‐posed problem
Regularization
Regularization methods
space‐fractional backward diffusion problem
Time dependence
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Summary:In this paper, we consider a Riesz–Feller space‐fractional backward diffusion problem with a time‐dependent coefficient ut(x,t)=ℓ(t)xDθγu(x,t)+f(x,t),(x,t)∈R×(0,T). We show that this problem is ill‐posed; therefore, we propose a convolution regularization method to solve it. New error estimates for the regularized solution are given under a priori and a posteriori parameter choice rules, respectively. Copyright © 2016 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4284