| 反向热传导问题的一种新的正则化方法 |
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| 引用本文： | 程炜,侯长顺,傅初黎. 反向热传导问题的一种新的正则化方法[J]. 数学的实践与认识, 2011, 41(4) |
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| 作者姓名： | 程炜 侯长顺 傅初黎 |
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| 作者单位： | 1. 河南工业大学,理学院,河南,郑州,450001
2. 兰州大学,数学与统计学院,甘肃,兰州,730000 |
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| 基金项目： | 国家自然科学基金(10671085); 河南省自然科学基金(102300410118); 河南省教育厅自然科学基金(2009B110007); 河南工业大学博士基金(2007BS028) |
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| 摘 要： | 讨论一个高维反向热传导问题,这是一个经典的严重不适定问题.关于这一问题我们给出一种新的正则化方法-改进的Tikhonov正则化方法,以恢复解对数据的连续依赖性.通过构造一个重要的不等式和提高先验光滑条件,获得正则解在0
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| 关 键 词： | 不适定问题 反向热传导问题 正则化 误差估计 |
A New Regularization Method for a Backward Heat Conduction Problem |
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| CHENG Wei,HOU Chang-shun,FU Chu-li. A New Regularization Method for a Backward Heat Conduction Problem[J]. Mathematics in Practice and Theory, 2011, 41(4) |
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| Authors: | CHENG Wei HOU Chang-shun FU Chu-li |
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| Affiliation: | CHENG Wei~1,HOU Chang-shun~1,FU Chu-li~2 (1.College of Science,Henan University of Technology,Zhengzhou 450001,China) (2.School of Mathematics and Statistics,Lanzhou University,Lanzhou 730000,China) |
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| Abstract: | This paper deals with a backward heat conduction problem in n-dimensional region,it is a classical severely ill-posed problem.we propose a new regularization method-modified Tikhonov regularization method for this problem to recover the stability of solution. Moreover,by introducing a rather technical inequality and improving a-priori smoothness assumption we obtain a quite sharp error estimate between the approximate solution and exact solution in interval 0
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| Keywords: | Ill-posed problem backward heat conduction problem regularization error estimation |
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