ANALYSIS AND DISCRETIZATION FOR AN OPTIMAL CONTROL PROBLEM OF A VARIABLE-COEFFICIENT RIESZ-FRACTIONAL DIFFUSION EQUATION WITH POINTWISE CONTROL CONSTRAINTS

作     者：周兆杰 王方圆 郑祥成 Zhaojie ZHOU;Fangyuan WANG;Xiangcheng ZHENG

作者机构：School of Mathematics and StatisticsShandong Normal UniversityJinan 250014China School of MathematicsShandong UniversityJinan 250100China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2023年第43卷第2期

页      面：640-654页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0701[理学-数学] 071101[理学-系统理论] 0811[工学-控制科学与工程] 

基　　金：supported by the National Natural Science Foundation of China(11971276,12171287) Natural Science Foundation of Shandong Province(ZR2016JL004) supported by the China Postdoctoral Science Foundation(2021TQ0017,2021M700244) International Postdoctoral Exchange Fellowship Program(Talent-Introduction Program)(YJ20210019) 

主　　题：Riesz-fractional diffusion equation variable coefficient optimal control finite element method Garding inequality optimal-order error estimate 

摘      要：We present a mathematical and numerical study for a pointwise optimal control problem governed by a variable-coefficient Riesz-fractional diffusion *** to the impact of the variable diffusivity coefficient,existing regularity results for their constantcoefficient counterparts do not apply,while the bilinear forms of the state(adjoint)equation may lose the coercivity that is critical in error estimates of the finite element *** reformulate the state equation as an equivalent constant-coefficient fractional diffusion equation with the addition of a variable-coefficient low-order fractional advection *** order optimality conditions are accordingly derived and the smoothing properties of the solutions are analyzed by,e.g.,interpolation *** weak coercivity of the resulting bilinear forms are proven via the Garding inequality,based on which we prove the optimal-order convergence estimates of the finite element method for the(adjoint)state variable and the control *** experiments substantiate the theoretical predictions.