非齐次热传导方程逆时问题的一种正则化方法  

A Regularization Method for A Backward Problem of Non-homogeneous Heat Equations

作　　者：何杰[1] 王泽文[1] 张文[1] 

机构地区：[1]东华理工大学数学与信息科学学院,江西抚州344000

出　　处：《宁夏大学学报（自然科学版）》2011年第3期198-201,共4页Journal of Ningxia University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10861001);江西省自然科学基金资助项目(2009GZS0001)

摘　　要：考虑了一类非齐次热传导方程的逆时问题,它是个典型的不适定问题.通过将方程的非齐次项和T时刻的温度场u(x,T)作Fourier展开,构造出正则化的近似问题,从而获得原逆时问题的正则化解,并给出了正则化解的稳定性估计和收敛性估计.最后,用数值例子说明该正则化方法是可行的.A backward problem of non-homogeneous heat conduction equations is considered, which is a typical ill-posed problem. By the Fourier expansions of the non-homogeneous term and the final temperature u（x, T） , a regularizing approximate problem is constructed, then a regularization solution of the original backward problem is obtained. Furthermore, the error estimates of the stability and the convergence for the regularization solution are presented. Finally, numerical examples are given to show the feasible of the proposed regularization method.

关 键 词：正则化方法 热传导方程 逆时问题 不适定问题 

分 类 号：O411.1[理学—理论物理]