热传导方程小波解的点态收敛  

Pointwise Convergence of the Wavelet Solution to the Parabolic Equation

作　　者：王晋茹[1] 

机构地区：[1]北京工业大学应用数理学院,北京100022

出　　处：《数学学报（中文版）》2006年第4期809-818,共10页Acta Mathematica Sinica：Chinese Series

基　　金：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)

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．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.

关 键 词：多分辨率分析 Meyer小波 小波解 

分 类 号：O174.2[理学—数学]