| 一个非标准逆热传导方程的正则化方法 |
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| 引用本文： | 王海龙,张选德.一个非标准逆热传导方程的正则化方法[J].宁夏师范学院学报,2006,27(6):27-30. |
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| 作者姓名： | 王海龙 张选德 |
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| 作者单位： | 1. 宁夏师范学院,数学与计算机科学系,宁夏,固原,756000
2. 宁夏大学,数学计算机学院,宁夏,银川,750021 |
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| 摘 要： | 考虑了一维抛物型方程的定解问题.问题是不适定性的,即g(t)微小扰动会引起解的很大误差.本文给出了利用Meyer小波的尺度函数在频域中形式作为窗函数来滤除g(t)的高频成分来正则化问题并给出了误差估计,与已有方法进行了比较和讨论.
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| 关 键 词： | 逆问题 不适定问题 抛物型方程 窗函数 正则化. |
| 文章编号： | 1001-0491（2006）06-0027-04 |
| 收稿时间： | 2006-03-06 |
| 修稿时间： | 2006年3月6日 |
Regularization for an Inverse Problem of Parabolic Equation |
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| WANG Hai-long,ZHANG Xuan-de.Regularization for an Inverse Problem of Parabolic Equation[J].Journal of Ningxia Teachers College,2006,27(6):27-30. |
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| Authors: | WANG Hai-long ZHANG Xuan-de |
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| Institution: | 1 Department of Mathematics and Computer Science, Ningxia Normal College, Ning Xia, Guyuan, China 756000; 2 Department of Mathematics and Computers, Ningxia University, Ning Xia, Yinchuan, China, 750021 |
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| Abstract: | The sideways parabolic equation in the quarter plane is considered.This is an illposed problem:a small perturbation in the data g(t) may cause dramatically large errors in the solution.Regularization for the problem is given by using the scaling function of Meyer wavelet as a window function to filter away highfrequence components of g(t).The error estimate also is provided.Then comparison and discussion between this method and the method in reference are given. |
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| Keywords: | Inverse Problem Ill-posed Problem Parabolic equation Window function Regularization |
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