一个非标准热方程反向问题的最优滤波正则化方法  

Optimal Filtering Regularization Method for a Non-standard Backward Heat Equation

作　　者：高翔[1] 傅初黎[1] 钱志[1] 熊向团[1] 闫亮[1] 

机构地区：[1]兰州大学数学与统计学院

出　　处：《工程数学学报》2008年第1期35-43,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10671085);甘肃省自然科学基金(3ZS051-A25-015);兰州大学理论物理与数学纯基础科学基金(Lzu05-05)

摘　　要：本文讨论一类非标准反向热传导问题。它是严重不适定的,即如果问题的解存在,其解将不连续依赖于数据。为了获得稳定的数值解,我们给出了一种最优滤波正则化方法,并对空间无界和有界两种情形进行了研究。我们分别对空间无界和有界情形采用了Fourier变换技术和分离变量方法,并均获得了最优的稳定性误差估计。此外,我们还给出了两个有趣的数值例子验证了所提出的正则化方法的有效性。We discuss in this paper a non-standard backward heat conduction problem （BHCP） which is severely ill-posed in the sense that the solution （if it exists） does not depend continuously on the data. In order to obtain stable numerical solution, we propose an optimal filtering regularization method. We investigate the ill-posed BHCP in the cases of spatial unbound and spatial bound. The Fourier transform technique is employed for the case of spatial unbound and the separation of variables for the case of spatial bound. For both eases, we obtain optimal stability error estimates. In addition, two interesting numerical examples are provided to show the effectiveness of the proposed regularization method.

关 键 词：反向热传导问题 不适定问题 滤波正则化 Ho1der稳定性 误差估计 

分 类 号：O175[理学—数学]