学术
摘 要:
我们考虑问题K（x）uxx=ua.0＜X〈1，t≥0，其中K（x）≥a≥0，u（0，t）=g，ix（0，t）=0．这是一个不适当的方程，因为当解存在时在边界g上一个小的扰动将对它的解造成很大的改变．我们考虑存在解u（x，·）∈L^2（R）用小波伽辽金方法和Meyer多分辨分析去滤掉高频部分，从而在尺度空间Vj上得到适定的近似解．我们也可以得到问题的准确解与它在Vj上的正交投影之间的误差估计．[著者文摘]
文章出处:
《应用数学》-2007年20卷3期 -512-518页
分 类 号:
文献标识码:
A
文章编号:
1001-9847（2007）03-0512-07
A Wavelet Galerkin Method Applied to Wave Equations with Variable Coefficients
OUAN Yu-xi SHI Zhi （School of Science,Xi＇an Univ. of Arch.＆ Tech. ,Xi＇an 710055, China）
Abstract:
We consider the problem K（x）ua = ua, 0〈x〈1, t≥0 , where K（x） is bounded below by a positive constant. The solution on the boundary x = 0 is a known function g and ux （0,t） = 0. This is an ill-posed problem in the sense that a small disturbance on the boundary specification g can produce a big alteration on its solution,if it exists. We consider the existence of a solution u（x,·） ∈ L^2 （R） and we use a wavelet Galerkin method with the Meyer multi-resolution analysis, to filter away the high-frequencies and to obtain well-posed approximating problems in the scaling spaces V~ . We also derive an estimate for the difference between the exact solution of the problem and the orthogonal projection onto Vj .[著者文摘]
Key words:
Wavelet ; Multi-resolution analysis ; Galerkin method
基金资助:
Supported by The National Natural Science Foundation of China（10071068）
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