On a Riesz-Feller space fractional backward diffusion problem with a nonlinear source

摘要

In this paper, a backward diffusion problem for a space-fractional diffusion equation with a nonlinear source in a strip is investigated. This problem is obtained from the classical diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha is an element of (0, 2]. A nonlinear problem is severely ill -posed, therefore we propose two new modified regularization solutions to solve it. We further show that the approximated problems are well-posed and their solutions converge if the original problem has a classical solution. In addition, the convergence estimates are presented under a priori bounded assumption of the exact solution. For estimating the error of the proposed method, a numerical example has been implemented. (C) 2016 Elsevier B.V. All rights reserved.