一类非线性抛物型方程反问题的变分伴随方法及其数值模拟  

On the Variational Adjoint Method and Numerical Simulation for A Class of Inverse Problems for Nonlinear Parabolic Equations

作　　者：王兵贤[1] 徐定华[1] 葛美宝[1] 

机构地区：[1]东华理工大学数学与信息科学学院,江西抚州344000

出　　处：《宁夏大学学报（自然科学版）》2008年第1期9-13,共5页Journal of Ningxia University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10561001);江西省自然科学基金资助项目(0511005);东华理工大学校长基金资助项目(DHXK0702)

摘　　要：利用偏微分方程最优控制中的伴随方法研究一类非线性抛物型方程逆时反问题.根据正则化思想改造最小二乘方法,依据变分伴随思想构造迭代算法.数值模拟试验验证了理论算法的可靠性.A class of inverse problems for nonlinear parabolic equations is discussed by the variational adjoint method, which is firstly proposed in optimization control for partial differential equations. The least squared method is modified by means of the idea of regularization and a new iteration algorithm is derived by using the variational adjoint method. The numerical simulation experiments show the validity and efficiency of the theoretical algorithm.

关 键 词：非线性抛物型方程 反问题 变分伴随方法 数值解 

分 类 号：O175.24[理学—数学]