An Inverse Source Problem with Sparsity Constraint for the Time-Fractional Diffusion Equation. Issue 1 (21st December 2015)

• Record Type: Journal Article
• Authors: Ruan, Zhousheng; Yang, Zhijian; Lu, Xiliang
• Is Part Of: Advances in applied mathematics and mechanics. Volume 8:Issue 1(2016)
• Page Start: 1
• Page End: 18
• Publication Date: 2015-12-21
• Subjects: 65N21, -- 49M15; Inverse source problem, -- time-fractional diffusion equation, -- sparse constraint, -- elastic-net regularization method, -- semismooth Newton method; Engineering mathematics -- Periodicals; Mechanics -- Periodicals; 620.00151825
• DOI: 10.4208/aamm.2014.m722
• Languages: English
• ISSNs: 2070-0733

Abstract

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.