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A Riesz–Feller space‐fractional backward diffusion problem with a time‐dependent coefficient: regularization and error estimates
Author(s) -
Tuan Nguyen Huy,
Trong Dang Duc,
Hai Dinh Nguyen Duy,
Thanh Duong Dang Xuan
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4284
Subject(s) - mathematics , regularization (linguistics) , a priori and a posteriori , convolution (computer science) , space (punctuation) , fractional calculus , mathematical analysis , diffusion , philosophy , linguistics , epistemology , artificial intelligence , machine learning , computer science , artificial neural network , physics , thermodynamics
In this paper, we consider a Riesz–Feller space‐fractional backward diffusion problem with a time‐dependent coefficientu t ( x , t ) = ℓ ( t )xD θ γ u ( 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.