华东师范大学学报(自然科学版) ›› 2008, Vol. 2008 ›› Issue (3): 21-29,3.

• 数学 统计学 • 上一篇    下一篇

一类奇摄动三阶常微分方程组的两点边值问题

徐洁1,2, 陈丽华3, 倪明康1,2

  

  1. 1. 华东师范大学 数学系, 上海 200062 2. 上海高校计算科学 E-研究院 上海交通大学研究所, 上海 200030 3. 福建师范大学福清分校, 福州 350300
  • 收稿日期:2007-06-04 修回日期:2007-10-23 出版日期:2008-05-25 发布日期:2008-05-25
  • 通讯作者: 徐洁

Boundary value problem of a class of third order differential equations(Chinese)

XU Jie1,2, CHEN Li-hua3, Ni Ming-kang1,2   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200062, China 2. SJTU Section, Computational Science Division, E-Institute of Shanghai Universities, Shanghai 200030, China 3. Fuqing Branch of Fujian Normal University, Fuzhou 350300, China
  • Received:2007-06-04 Revised:2007-10-23 Online:2008-05-25 Published:2008-05-25

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摘要： 利用边界层函数法构造了一类奇摄动三阶方程组两点边值问题的渐近解, 并严格证明了解的存在惟一性及其渐近解的一致有效性.

关键词: 奇摄动, 渐近展开, 边界层函数, 不变流形, 奇摄动, 渐近展开, 边界层函数, 不变流形

Abstract: This paper, using the method of boundary functions, studied boundary value problem of a class of singularly perturbed third order differential equations. At the same time the asymptotice solution of the problem was given and the uniform validity of its asymptotic solution was proved in a rigorous way.

Key words: asymptotic expansion, boundary layer function, unchange manifold, singular perturbation, asymptotic expansion, boundary layer function, unchange manifold

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