中文摘要：

考虑确定热流ux（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（21/2-（π/3）1/2）/22〈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.

英文摘要：

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.