初始场与边界热流同时识别反问题的正则化方法  

Regularization Method for Simultaneous Identificationof Initial Field and Boundary Heat Flow

作　　者：赵宇星 徐定华[1] ZHAO Yuxing;XU Dinghua(School of Science,Zhejiang Sci-Tech University,Hangzhou 310018,China)

机构地区：[1]浙江理工大学理学院,杭州310018

出　　处：《吉林大学学报（理学版）》2022年第3期543-551,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11871435).

摘　　要：考虑含Neumann边界条件的一维热方程的初始场与边界热流同时识别反问题.首先,给定右边界热流密度及温度值和终止时刻温度值,建立Fredholm积分方程组模型,证明其解的唯一性.其次,构造左边界热流密度与初始温度场同时反演的正则化算法.数值实例结果表明,采取的数据预处理算法及改进正则化方法,双函数反演的精度更高.We considered an inverse problem of simultaneous identification of the initial field and boundary heat flux for one-dimensional heat equation with Neumann boundary conditions.Firstly,the heat flux density and temperature at the right boundary and the terminal temperature were given,a model of Fredholm integral equation was established and the uniqueness of its solution was proved.Secondly,a regularization method for simultaneous inversion of the heat flux density at the left boundary and initial temperature field was constructed.The results of numerical examples show that the data preprocessing algorithm and improved regularization method achieve higher accuracy of double-function inversion.

关 键 词：反问题 热传导方程 NEUMANN边界条件 积分方程组 正则化方法 

分 类 号：O242.1[理学—计算数学]