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

作者：Wei, T.^*; Li, X. L.; Li, Y. S.

来源：Inverse Problems, 2016, 32(8): 085003.

DOI：10.1088/0266-5611/32/8/085003

• inverse source problem
• fractional diffusion equation
• conjugate gradient method

This paper is devoted to identifying a time-dependent source term in a multidimensional 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.

• 出版日期2016-8
• 单位兰州大学