Acta Mathematica Vietnamica

, Volume 43, Issue 3, pp 449–470

# The Backward Problem for a Nonlinear Riesz-Feller Diffusion Equation

Article

## Abstract

In this paper, we reconstruct the solution u(x,t) of the backward space-fractional diffusion problem with a locally Lipschitzian nonlinear source

This problem is severely ill-posed in the Hadamard sense, hence, a regularization is in order. In the paper, we introduce one spectral regularization method and establish stability error estimates with optimal order under an a priori choice of regularization parameter. Finally, numerical implementations are given to show the effectiveness of the proposed regularization methods.

## Keywords

Space-fractional backward diffusion problem Ill-posed problem Regularization Error estimate

## Mathematics Subject Classification (2010)

26A33 47A52 47J06 65M32

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