华东师范大学学报(自然科学版) ›› 2008, Vol. 2008 ›› Issue (3): 12-20.

• 数学 统计学 • 上一篇    下一篇

一类三阶方程的奇摄动边值问题

陈丽华1,2, 徐洁2, 倪明康2,3   

  1. 1. 福建师范大学福清分校 数学与计算机科学系, 福州福清 350300; 2. 华东师范大学 数学系, 上海 200062; 3. 上海高校计算科学E-研究院 上海交通大学研究所, 上海 200030
  • 收稿日期:2007-06-15 修回日期:2007-12-07 出版日期:2008-05-25 发布日期:2008-05-25
  • 通讯作者: 倪明康

Singularly perturbed BVP for third nonlinear ODE(Chinese)

CHEN Li-hua1,2, XU Jie2, NI Ming-kang2,3   

  1. 1. Math ematics and Computer Science Department, Fuqing Branch of Fujian Normal University, Fujian 350300, China;2. Department of Mathematics, East China Normal University, Shanghai 200062, China;3. SJTU Section, Computational Science Division, E-Institute of Shanghai Universities, Shanghai 200030, China
  • Received:2007-06-15 Revised:2007-12-07 Online:2008-05-25 Published:2008-05-25
  • Contact: NI Ming-kang

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摘要：

利用边界层函数法研究一类非线性三阶奇摄动方程的边值问题. 当gy′>0时,首先将所论问题转化成等价的Tikhonov方程组边值问题，然后构造了它的双边界层渐近解,并证明了所有边界函数的指数式衰减特性.最后给出了所论问题解的存在唯一性以及渐近解的余项估计.当gy′<0时，简要地说明了为什么本问题一般无解.

关键词: 奇异摄动, 边界函数, 不变流形, 渐近分析, 奇异摄动, 边界函数, 不变流形, 渐近分析

Abstract:

This paper studied a kind of BVP of nonlinear third order singularly perturbed equations by boundary layer function method. When gy′>0, at first, the problem was turned to a BVP of equivalent Tikhonov system. Then the asymptotic solution of doubly boundary layer for the system was constructed, and the character of exponential decay for all boundary functions was proved. Finally the main results of this paper: existence and uniqueness of solution and estimation of remainder for the problem are given. When gy′<0, in general, there is no solution to this problem.

Key words: boundary functions, invariant manifold, asymptotic analysis, singular perturbation, boundary functions, invariant manifold, asymptotic analysis

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