@Article{AAMM-8-1, author = {Ruan , ZhoushengYang , Zhijian and Lu , Xiliang}, title = {An Inverse Source Problem with Sparsity Constraint for the Time-Fractional Diffusion Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {1}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m722}, url = {http://global-sci.org/intro/article_detail/aamm/12073.html} }