数值重构二阶抛物型方程的一阶项系数  

Numerical Reconstruction for the First-order Coefficient of the Second Order Parabolic Equation

作　　者：任建龙[1] 曾剑[1] 甄苇苇 REN Jian long;ZENG Jian;ZHEN Wei wei(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《兰州交通大学学报》2018年第4期99-104,共6页Journal of Lanzhou Jiaotong University

基　　金：国家自然科学基金(11261029;11461039);甘肃省自然科学基金(145RJZA124)

摘　　要：研究了一个利用附加条件反演二阶抛物型方程一阶项系数的反问题,基于最优控制框架,证明了控制泛函极小元的存在性及其满足的必要条件.在正问题的计算中,运用离散的有限差分格式来计算方程的数值解,并且用Gradient型迭代法进行数值模拟.数值结果表明该算法是稳定的,而且未知系数反演的效果也很好.This paper investigated an inverse problem of using the additional conditions to reconstruct the first-order coefficient of the second order parabolic equation.Based on the optimal control framework,the existence of the minimize of the cost functional was proved,and the necessary condition which must be satisfied by the minimize was deduced.In the calculation of the forward problem,the numerical solution of the equation was calculated through a discrete finite difference scheme,used to and numerical simulation was conducted by using the Gradient iterative method.The numerical results show that the algorithm designed in this paper is stable and the inversion effect of unkonwn coefficients is very good.

关 键 词：反问题 最优控制 必要条件 有限差分 Gradient型迭代 

分 类 号：O175.26[理学—数学]