二维时间反向热传导问题的正则化方法及误差估计  

The Regularization Methods for Solving the Time-Inverse Heat Conduction Problems in Two Dimensions and Error Estimation

作　　者：侯佳琪 熊向团 HOU Jiaqi;XIONG Xiangtuan(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《四川师范大学学报（自然科学版）》2023年第4期497-502,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11661072)。

摘　　要：讨论二维时间反向热传导问题,从终值时刻t=T(T>0)的温度分布来反演初始时刻的温度分布.该问题在图像处理方面有重要应用.这是一个严重不适定问题,它的解在一定条件下不连续依赖于数据.针对传统正则化方法的缺陷,采用拟逆正则化方法和分数次Tikhonov正则化方法恢复解对数据的依赖性.同时,还给出2种方法相应的先验参数选取规则及其正则解与精确解的误差估计.In this paper,we discuss the problem of time-inverse heat conduction in two-dimensional space,which is used to re-trieve the temperature distribution from that the final moment t=T(T>0).One of the most important application area of the problem is image deblurring.This problem is a serious ill-posed problem,i.e.its solution is not continuously dependent on the data under cer-tain conditions.So the quasi-reversibility regularization method and the fractional Tikhonov regularization method are proposed to re-store the dependence of the solution on the data.Meanwhile,the errors between the approximate solutions and the exact solution for the ill-posed problem are estimated,and the selection rules based on the priori regularization parameter are given.

关 键 词：不适定问题 时间反向热传导问题 分数次Tikhonov正则化方法 拟逆正则化方法 正则化先验参数选取 误差估计 

分 类 号：O241.8[理学—计算数学]