Numerical reconstruction of the spatial component
in the source term of a time-fractional diffusion
In this article, we are concerned with the analysis on the numerical reconstruction
of the spatial component in the source term of a time-fractional diffusion equation.
This ill-posed problem is solved through a stabilized nonlinear minimization system
by an appropriately selected Tikhonov regularization. The existence and the stability
of the optimization system are demonstrated. The nonlinear optimization problem is
approximated by a fully discrete scheme, whose convergence is established under a
novel result verified in this study that the H 1 -norm of the solution to the discrete forward system is uniformly bounded. The iterative thresholding algorithm is proposed to solve the discrete minimization, and several numerical experiments are presented to show the efficiency and the accuracy of the algorithm.
蒋代军，华中师范大学副教授，2007年获得华中师范大学学士学位，2009年和2012年分别获得武汉大学硕士和博士学位。蒋代军博士的研究领域包括偏微分方程反问题、稀疏优化及控制，快速算法等，主持国家自然科学基金项目3项，在SIAM J. Appl. Math., Journal of Differential Equations, Inverse Problems, Inverse Problems and Imaging等国际知名刊物上发表论文20余篇。