Paper Info
Title
An inverse time-dependent source problem for a time-space fractional diffusion equation.
Abstract
This paper is devoted to identify a time-dependent source term in a time–space fractional diffusion equation by using the usual initial and boundary data and an additional measurement data at an inner point. The existence and uniqueness of a weak solution for the corresponding direct problem with homogeneous Dirichlet boundary condition are proved. We provide the uniqueness and a stability estimate for the inverse time-dependent source problem. Based on the separation of variables, we transform the inverse source problem into a first kind Volterra integral equation with the source term as the unknown function and then show the ill-posedness of the problem. Further, we use a boundary element method combined with a generalized Tikhonov regularization to solve the Volterra integral equation of the fist kind. The generalized cross validation rule for the choice of regularization parameter is applied to obtain a stable numerical approximation to the time-dependent source term. Numerical experiments for six examples in one-dimensional and two-dimensional cases show that our proposed method is effective and stable.
Year
DOI
Venue
2018
10.1016/j.amc.2018.05.016
Applied Mathematics and Computation
Keywords
Field
DocType
Inverse source problem,Time–space fractional diffusion equation,Tikhonov regularization method,Boundary element method
Tikhonov regularization,Uniqueness,Mathematical analysis,Dirichlet boundary condition,Dependent source,Weak solution,Boundary element method,Separation of variables,Mathematics,Volterra integral equation
Journal
Volume
ISSN
Citations 
336
0096-3003
0
PageRank 
References 
Authors
0.34
4
2
Name
Order
Citations
PageRank
Youping Li121.39
T. Wei28718.96