An inverse time-dependent source problem for a time-fractional diffusion equation ☆This paper was supported by the NSF of China (11371181) and the Fundamental Research Funds for the Central Universities (lzujbky-2013-k02). (14th June 2016)

• Record Type: Journal Article
• Authors: Wei, T; Li, X L; Li, Y S
• Is Part Of: Inverse problems. Volume 32:Number 8(2016:Aug.)
• Publication Date: 2016-06-14
• Subjects: inverse source problem -- fractional diffusion equation -- conjugate gradient method; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/8/085003
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: This paper is devoted to identifying a time-dependent source term in a multi-dimensional time-fractional diffusion equation from boundary Cauchy data. The existence and uniqueness of a strong solution for the corresponding direct problem with homogeneous Neumann boundary condition are firstly proved. We provide the uniqueness and a stability estimate for the inverse time-dependent source problem. Then we use the Tikhonov regularization method to solve the inverse source problem and propose a conjugate gradient algorithm to find a good approximation to the minimizer of the Tikhonov regularization functional. Numerical examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed method.