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

Abstract

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.

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