具有快慢变量的方程组的阶梯状空间对照结构

J4 ›› 2013, Vol. 48 ›› Issue (2): 98-104.

具有快慢变量的方程组的阶梯状空间对照结构

王爱峰1,2

1.淮阴师范学院数学科学学院, 江苏淮安 223300;
2.华东师范大学数学系, 上海 200062

收稿日期:2012-04-24 出版日期:2013-02-20 发布日期:2013-03-04
作者简介:王爱峰(1976- ), 女, 博士, 副教授, 研究方向为常微分方程奇异摄动理论. Email: waf2003@126.com
基金资助:
上海市自然科学基金资助项目(10ZR1409200)；上海市教育委员会E研究院建设项目(N.E03004)

The steptype contrast structure for a singularly perturbed system with slow and fast variables

WANG Ai-feng1,2

1. School of Mathematical Science, Huaiyin Normal University, Huaian 223300, Jiangsu, China;
2. Department of Mathematics, East China Normal University, Shanghai 200062, China

Received:2012-04-24 Online:2013-02-20 Published:2013-03-04

摘要/Abstract

摘要：

讨论了具有快慢变量的方程组的阶梯状空间对照结构。利用首次积分来构造所需要的异宿轨道并确定对照结构发生的转移点的位置,用边界函数法构造形式渐近解并用缝接法证明了阶梯解的存在性和形式渐近解的一致有效性。

关键词: 奇异摄动; 阶梯状空间对照结构; 边界函数; 首次积分

Abstract:

The step-type contrast structure for a singularly perturbed system with slow and fast variables is considered. We not only construct the heteroclinic orbit by first integral, but also determine the internal transition time t. The asymptotic expansion of this problem with a step-type contrast structure is constructed by the boundary function method. By sewing orbit smooth, the existence of the step-type contrast structure is shown and the asymptotic solution is proved to be uniformly in the whole interval.

Key words: singulary perturbed; step-type contrast structure; boundary function; first integral

王爱峰1,2. 具有快慢变量的方程组的阶梯状空间对照结构[J]. J4, 2013, 48(2): 98-104.

WANG Ai-feng1,2. The steptype contrast structure for a singularly perturbed system with slow and fast variables[J]. J4, 2013, 48(2): 98-104.

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