双曲-抛物奇异摄动问题的O（ε^n）阶渐近展开  

An Asymptotic Expansion for Quasi-liner Singular Perturbation Problem of Hyperbolic-Parabolic Partial Differential Equation

作　　者：陈国玉[1] 沈锦仁[2] 王雪琴[1] 魏小燕[1] 张秋田[1] 

机构地区：[1]解放军炮兵学院基础部,安徽合肥230001 [2]解放军理工大学理学院,江苏南京211101

出　　处：《甘肃科学学报》2009年第3期29-32,共4页Journal of Gansu Sciences

基　　金：解放军炮兵学院青年后备人才基金(20070523)

摘　　要：为讨论一个双曲-抛物奇异摄动问题的渐近展开问题,首先用能量方法建立稳定不等式,然后利用双重迭代法对原问题进行渐近展开,最后用稳定不等式证明了渐近解对原问题解的O(εn)阶逼近式,从而证明了渐近解的一致有效性.A singular perturbation problem of a hyperbolic-parabolic partial differential equation is dis- cussed. In order to solve the asymptotic expansion of the problem, the energy method is applied to establish the continuous stability inequality and the n-order asymptotic expansion of the solution to this problem with respect to small parameters. Thus the uniform effectiveness of the asymptotic expansion is proved.

关 键 词：奇异摄动问题 双曲-抛物偏微分方程 连续稳定不等式 小参数 

分 类 号：O175.1[理学—数学]