| 热传导方程小波解的点态收敛 |
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| 引用本文： | 王晋茹.热传导方程小波解的点态收敛[J].数学学报,2006,49(4):809-818. |
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| 作者姓名： | 王晋茹 |
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| 作者单位： | 北京工业大学应用数理学院,北京100022 |
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| 基金项目： | 北京市教委基金资助项目（KM200410005013）;北京工业大学数理基金资助项目（KZ0601200383）;致谢 本文是在导师刘有明教授的悉心指导下完成的,作者在此表示深切地谢意.另外,作者感谢审稿人对本文提出得宝贵修改意见. |
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| 摘 要： | 本文主要考虑热传导方程uxx=ut,0≤x<1,t≥0;u(1,t)=g(t),其中边界条件g(t)为已知函数．此定解问题为一不适定问题,也就是说当边界条件有微小扰动时,将会引起解大的扰动．本文将利用多分辨率分析构造一小波解,且证明此解是适定的,并给出所定义小波解与定解问题的真正解在点态意义下的误差估计．
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| 关 键 词： | 多分辨率分析 Meyer小波 小波解 |
| 文章编号： | 0583-1431（2006）04-0809-10 |
| 收稿时间： | 2004-08-23 |
| 修稿时间： | 2004-08-232005-05-20 |
Pointwise Convergence of the Wavelet Solution to the Parabolic Equation |
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| Jin Ru WANG.Pointwise Convergence of the Wavelet Solution to the Parabolic Equation[J].Acta Mathematica Sinica,2006,49(4):809-818. |
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| Authors: | Jin Ru WANG |
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| Institution: | College of Applied Mathematics and Physics, Beijing University of Technology, Beijing 100022, P. R. China |
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| Abstract: | We consider the problem uxx= ut,0≤x<1, t≥0. The solution on the boundary x = 1 is a known function g(t). This is an ill-posed problem in the sense that a small disturbance on the boundary g(t) can produce a big alternation on its solution (if it exists). We shall define a wavelet solution with the Meyer multi-resolution analysis to obtain well-posed approximating problem in the scaling space Vj. We shall also give an estimate for the difference between the exact solution of the problem and the defined wavelet solution. |
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| Keywords: | multi-resolution analysis Meyer wavelet wavelet solution |
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