@Article{AAMM-8-1,
author = {Zhousheng, Ruan and Zhijian, Yang and Xiliang, Lu},
title = {An Inverse Source Problem with Sparsity Constraint for the Time-Fractional Diffusion Equation},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2016},
volume = {8},
number = {1},
pages = {1--18},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2014.m722},
url = {https://global-sci.com/article/73317/an-inverse-source-problem-with-sparsity-constraint-for-the-time-fractional-diffusion-equation}
}