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

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• 作者：Nguyen Huy Tuan^a ; Dinh Nguyen Duy Hai^b ; Le Dinh Long^c ; Van Thinh Nguyen^d ; Mokhtar Kirane^e ; ^f ; ^{mokhtar.kirane@univ-lr.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Space-fractional backward diffusion problem ; Ill-posed problem ; Regularization ; Error estimate
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：312
• 期：Complete
• 页码：103-126
• 全文大小：4629 K

文摘

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 α∈(0,2]$\alpha \in (0,2]$. 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.