An inverse time-dependent source problem for a time–space fractional diffusion equation

Y. S. Li and T. Wei

Applied Mathematics and Computation, 2018, vol. 336, issue C, 257-271

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.

Keywords: Inverse source problem; Time–space fractional diffusion equation; Tikhonov regularization method; Boundary element method (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:336:y:2018:i:c:p:257-271

DOI: 10.1016/j.amc.2018.05.016

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