一维有耗散波动方程的奇性分析与小波

对系数有强奇性（间断）的波动方程，用通常的线性化简的方法时往往会将数值小但奇性强的项略去，导致结果严重失真。利用小波变换这一工具，可以在化简时保留奇性的主要部分，使所得的结果从奇性分析的观点看来更为精确。此方法曾被用来处理系数有间断的一维波动方程，得到了与精确解的奇性主部完全一致的解．在本文中，我们改进了用小波变换作奇性化简的方法，对系数有间断的一维有耗散波动方程求得了与精确解奇性主部完全一致的解。这说明利用小波分析作奇性化简的方法对高频近似及奇性分析问题是普遍适用的．

ANALYSIS OF SINGULARITLES OF ONE-DIMENSIONAL WAVE EQUATIONS WITH DISSIPATIONS AND WAVELETS

Applying the usual technique of linearization to wave equations with strongsingularity often produces artifacts, for those terms with strong singularities are omittedfor they are small in magnitude. Using the method of wavelets transform, the main terms in singularities are retained in simplification. So the result is more accurate in a point view of singularity analysis. We have applied the mathod to one-dimensionalwave equations in inhomogeneous media, and got the same main terms in singularitiesas the accurate ones. In this paper, one-dimensional wave equations with dissipationsin inhomogeneous media are considered. The method of wavelets analysis is improved,and the same main terms in singularities as the accurate solutions are obtained as well。So we conclude applying wavelets analysis to singularity simplification is alwayseffective.especially to high-frequency approximation and singularity analysis.