兰州大学机构库 >数学与统计学院
一个含有对流项的逆热传导问题的Wavelet-Galerkin正则化方法
Alternative TitleWavelet-Galerkin Regularization Method for an Inverse Heat Conduction Problem with Convection Term
南楠
Subtype硕士
Thesis Advisor傅初黎
2005-05-20
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword逆热传导问题 不适定问题 正则化 Wavelet-Galerkin方法 误差估计
Abstract在许多实际问题中,常常需要从物体内部某个固定位置的温度测量数据来确定物体表面的温度分布,这就是所谓的逆热传导问题(IHCP).逆热传导问题是近年来反问题研究领域的热点和前沿课题,而目前对非标准逆热传导问题的理论结果甚少.本文研究一类特殊的非标准型逆热传导问题,即如下的含有对流项的抛物方程侧边值问题: { } 我们要利用x=1处的温度数据g(t)来确定区间[0,1)上的温度分布u(x,t).这是一类严重的不适定问题,数据的微小扰动就会引起解的巨大变化,使其数值实现极为困难. 由于在实际问题中g(t)往往是测量数据,必定存在测量误差,因此对这类问题给出有效的正则化方法就是一个非常有意义同时也极为困难的工作.本文给出了处理这一问题的一种新的Wavelet-Galerkin方法,获得了阶数最优的稳定性估计, 并且解决了零点的收敛性问题,大大改进了已有工作的结果.
Other AbstractIn many practical applications one wishes to determine the surface temperature from a measured temperature history at a fixed location inside a body. This problem is called inverse heat conduction problem (IHCP). At present, few theoretic results are available in the literature for non-standard inverse heat conduction problem. In this paper, we consider a class of special non-standard inverse heat conduction problem, i.e., a sideways parabolic equation with convection term as follows: { } We want to determine the solution u(x,t) for 0
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224539
Collection数学与统计学院
Recommended Citation
GB/T 7714
南楠. 一个含有对流项的逆热传导问题的Wavelet-Galerkin正则化方法[D]. 兰州. 兰州大学,2005.
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