Year: 2016
Author: Zhousheng Ruan, Zhijian Yang, Xiliang Lu
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 1 : pp. 1–18
Abstract
In this paper, an inverse source problem for the time-fractional diffusion equation is investigated. The observational data is on the final time and the source term is assumed to be temporally independent and with a sparse structure. Here the sparsity is understood with respect to the pixel basis, i.e., the source has a small support. By an elastic-net regularization method, this inverse source problem is formulated into an optimization problem and a semismooth Newton (SSN) algorithm is developed to solve it. A discretization strategy is applied in the numerical realization. Several one- and two- dimensional numerical examples illustrate the efficiency of the proposed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2014.m722
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 1 : pp. 1–18
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18