由抛物型积分微分方程方程所描述的最优控制问题在很多领域中具有广泛的应用，如：热传导问题、人口动力学问题、粘弹性力学、材料设计等问题，因此研究此类最优控制问题的数值求解具有十分重要的理论意义和应用价值。本项目在申请人博士学位论文的已有理论基础上，拟对受抛物型积分微分方程约束的分布最优控制问题，在控制积分受限和点态受限两种情况下，研究其自适应有限元高效数值方法。主要工作包括其积微分全离散格式的建立，相应的理论分析(等价的上界、下界后验误差估计，推导误差估计子等)，并结合具体模型，进行同套网格和不同套网格上的对比数值试验以发展高效的自适应有限元数值方法。在上述研究基础之上，本项目拟进一步发展抛物型积分微分方程边界最优控制问题的高效自适应有限元数值方法。

Optimal control problems governed by parabolic integro-differential equations is widely used in heat conduction, human population control,viscoelastic mechanics,material design and so on. Therefore its numerical methods are very important in real applications.Based on the Ph.D research of the applicant, this research proposal aims to develop high-performance adaptive finite element methods for the distributed optimal control governed by parabolic integro-differential equations under the control constraints of obstacle or integral type. The main work includes integro-differential discretization of the control problem, theoretical analysis (equivalent a posteriori error estimates, and estimators), and extensive numerical simulations on single and multi-meshes in order to develop high-performance adaptive finite element methods for the optimal control of this kind. Furthermore we will extend our research to the boundary optimal control problem governed by parabolic integro-differential equations.