The Backward Problem for a Nonlinear Riesz-Feller Diffusion Equation
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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.
KeywordsSpace-fractional backward diffusion problem Ill-posed problem Regularization Error estimate
Mathematics Subject Classification (2010)26A33 47A52 47J06 65M32
The authors would like to thank the referees for the careful reading, helpful comments and suggestions leading to the improved version of the paper.