報告題目： Uniqueness and numerical methods for inverse source problems in a time-fractional diffusion equation
報 告 人：蔣代軍副教授 華中師範大學
報告時間：2023年5月4日 14:00-15:00
報告地點：騰訊會議 ID：222-542-141
會議鍊接：https://meeting.tencent.com/dm/1a2ICZRAhMbQ
校内聯系人：刁懷安 diao @ jlu.edu.cn
報告摘要：In this talk, 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 H1 -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.
報告人簡介：蔣代軍，華中師範大學副教授，2007年獲得華中師範大學學士學位，2009年和2012年分别獲得武漢大學碩士和博士學位。蔣代軍博士的研究領域包括偏微分方程反問題、稀疏優化及控制，快速算法等，主持國家自然科學基金項目4項，在SIAM系列，Inverse Problems等刊物上發表學術論文近30篇。
