热传导方程反问题的一个逼近方法  

An approximation method for the inverse problem of the heat equation

作　　者：杨阿莉[1] 王连堂[1] 郭玉亮 

机构地区：[1]西北大学数学系 [2]咸阳技工学校,陕西咸阳712000

出　　处：《纺织高校基础科学学报》2006年第3期250-252,共3页Basic Sciences Journal of Textile Universities

基　　金：西安工程科技学院校管科研项目(2005XG37)

摘　　要：讨论了在某时刻温度分布已知的情况下,求解热传导方程第二类边值问题的初始条件反问题.在给出解的存在性与惟一性证明的基础上,采用Tikhonov正则化方法将其转化为非线性最优化问题,并用梯形公式对积分离散化进行数值求解.数值模拟结果表明该方法既可行且有效.The inverse problem of the initial condition of heat equation considered is determined if the temperature distribution inside a domain are known at some time. Based on the existence and uniqueness proof of solution, Tikhonov regularization method is used to convert the problem with Neuman boundary conditions into a nonlinear optimization problem. And integral operator is discretized by trapezoidal rule for an approximation solution. Numerical examples show that this method is both accurate and simple to use.

关 键 词：积分方程 正则化 最优化 离散化 

分 类 号：O175.26[理学—数学]