Volume 8, Issue 1
An Inverse Source Problem with Sparsity Constraint for the Time-Fractional Diffusion Equation

Zhousheng Ruan ,  Zhijian Yang and Xiliang Lu

10.4208/aamm.2014.m722

Adv. Appl. Math. Mech., 8 (2016), pp. 1-18.

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  • 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.

  • History

Published online: 2018-05

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