Acta Mathematica Vietnamica

, Volume 43, Issue 3, pp 449–470 | Cite as

The Backward Problem for a Nonlinear Riesz-Feller Diffusion Equation

  • Dinh Nguyen Duy Hai
  • Dang Duc TrongEmail author


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.


Space-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.

Funding information

This paper is supported by National Foundation of Scientific and Technology Development (NAFOSTED)-Project 101.02-2016.26.


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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceHo Chi Minh City National UniversityHo Chi Minh CityVietnam
  2. 2.Faculty of Basic ScienceHo Chi Minh City University of TransportHo Chi Minh CityVietnam

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