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The Backward Problem for a Nonlinear Riesz-Feller Diffusion Equation
Dinh Nguyen Duy Hai
,
Dang Duc Trong
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.