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

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]. 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

Title:	On a Riesz-Feller space fractional backward diffusion problem with a nonlinear source
Authors:	Nguyen Huy Tuan Dinh Nguyen Duy Hai Le Dinh Long Nguyen Van Thinh
Keywords:	Space-fractional backward diffusion problem Ill-posed problem Regularization Error estimate
Issue Date:	2017
Publisher:	ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
Citation:	ISIKNOWLEDGE
Abstract:	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]. 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
Description:	TNS06982 ; JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 312 Pages: 103-126 Published: MAR 1 2017
URI:	http://repository.vnu.edu.vn/handle/VNU_123/28416 http://www.sciencedirect.com/science/article/pii/S0377042716000078
ISSN:	0377-0427 1879-1778
Appears in Collections:	Bài báo của ĐHQGHN trong Web of Science