An Inverse Source Problem with Sparsity Constraint for the Time-Fractional Diffusion Equation

作者：Ruan, Zhousheng; Yang, Zhijian; Lu, Xiliang^*

来源：Advances in Applied Mathematics and Mechanics, 2016, 8(1): 1-18.

DOI：10.4208/aamm.2014.m722

• Inverse source problem
• time-fractional diffusion equation
• sparse constraint
• elastic-net regularization method
• semismooth Newton method

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.

• 出版日期2016-2
• 单位东华理工大学; 武汉大学