The Backward Problem for a Nonlinear Riesz-Feller Diffusion Equation

• DOI: 10.1007/s40306-018-0255-2
• Publication Date: 2018-03-27T07:34:20Z
• Authors: Dinh Nguyen Duy Hai; Dang Duc Trong
• Keywords: 0101 mathematics; 01 natural sciences

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.