确定热流的非标准逆热传导问题的小波正则化方法  

Wavelet Regularization Method for Determining Heat Flux of Non-standard Inverse Conduction Problem

作　　者：冯立新[1] 李媛[1] 

机构地区：[1]黑龙江大学数学系,哈尔滨150080

出　　处：《数学物理学报（A辑）》2012年第4期709-719,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(10801046);黑龙江省教育厅项目(11551364);黑龙江大学基金(Hdtd2010-14)资助

摘　　要：考虑确定热流u_x(x,t),0<x<1的非标准逆热传导问题这是严重的不适定问题.该文分析了问题的不适定性,利用Meyer小波给出了小波正则解,并且在(2^(1/2)-(π/3)^(1/2))/2^(2)<x<1时给出了正则解与精确解之间的H(o|¨)lder型误差估计,数值实验表明在0<x<1时正则解能够收敛到精确解.We consider the non-standard inverse heat conduction problem of determiniting the heat flux u_x（x,t）,0 〈 x 〈 1 from a measured temperature at x = 1 This problem is severely ill-posed.In this paper,we analyse the problem ill-posedness,give a wavelet regularization solution based on an application of Meyer wavelet.And error estimate with Holder type between the exact solution and the regularized solution is given at（2～（1/2） - （π/3）～（1/2）/2～（1/2） 〈 x 〈 1.The numerical experiment result shows that the regularization solution may converge to the exact solution for 0 〈 x 〈 1.

关 键 词：逆热传导问题 不适定问题 正则化 误差估计 Meyer小波 

分 类 号：O175.23[理学—数学]