报告题目 (Title)：Error analysis of spectral method for fractional optimal control problems (分数阶最优控制问题的谱方法的误差分析)

报告人 (Speaker)：陈艳萍 教授（南京邮电大学）

报告时间 (Time)：2024年6月4日(周二) 10:00-12:00

报告地点 (Place)：校本部F309

邀请人(Inviter)：李常品、蔡敏

主办部门：理学院数学系

报告摘要：In this talk, we investigate an optimal control problem governed by a time fractional diffusion equation with non-homogeneous boundary condition. We construct a suitable weak formulation, study its well-posedness, and develop a spectral Galerkin method for its numerical solution. The main contributions of this work are: 1) the study of optimality conditions, which is crucial for analyzing the optimal control problem; 2) the derivation of a priori error estimates for the space-time spectral approximation; 3) the derivation of a posteriori error estimates for the state, costate, and control approximations; 4) the conduct of numerical experiments to confirm the efficiency of the proposed method. The obtained numerical results demonstrate exponential convergence for smooth exact solutions.