Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8901668 | Journal of Computational and Applied Mathematics | 2019 | 20 Pages |
Abstract
In this paper, we investigate the problem of recovering the historical distribution for a nonlinear space-fractional diffusion equation with temporally dependent thermal conductivity in higher dimensional space. This problem is obtained from the classical diffusion equation by replacing the second-order space derivative with a fractional Laplacian of order αâ(1â2,1], which is usually used to model the anomalous diffusion. The problem is severely ill-posed. To regularize the problem, we propose a modified version of the Tikhonov regularization method. A stability estimate of Hölder type is established. Finally, several numerical examples based on the finite difference approximation and the discrete Fourier transform are presented to illustrate the theoretical results.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Tran Thi Khieu, Hoang-Hung Vo,