TY - JOUR
T1 - An Inverse Source Problem with Sparsity Constraint for the Time-Fractional Diffusion Equation
AU - Ruan , Zhousheng
AU - Yang , Zhijian
AU - Lu , Xiliang
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 1
EP - 18
PY - 2018
DA - 2018/05
SN - 8
DO - http://doi.org/10.4208/aamm.2014.m722
UR - https://global-sci.org/intro/article_detail/aamm/12073.html
KW - 
AB - <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>