王爱峰.具有边值条件的高维吉洪诺夫系统的阶梯状空间对照结构[J].数学年刊A辑,2017,38(4):433~446
具有边值条件的高维吉洪诺夫系统的阶梯状空间对照结构
The Step-Type Contrast Structure for High-Dimensional Tikhonov System with Boundary Conditions
Received: July 21, 2015  Revised: March 14, 2016
DOI:10.16205/j.cnki.cama.2017.0035
中文关键词:  Contrast structure, Singular perturbation, Asymptotic expansion, Boundary function
英文关键词:Contrast structure, Singular perturbation, Asymptotic expansion, Boundary function
基金项目:本文受到国家自然科学基金(No.11501236)的资助.
Author NameAffiliationE-mail
WANG Aifeng School of Mathematical Science, Huaiyin Normal University, Huai'an 223001, Jiangsu, China. waf2003@126.com 
Hits: 151
Download times: 169
中文摘要:
      借助于首次积分构造高维的空间异宿轨道, 利用指数二分法的一些性质和Fredholm 交换引理,在求解高阶边界函数的同时确定了转移点$t^*$. 利用边界函数法构造形式渐近解, 用 $k+\sigma$ 交换引理证明了高维吉洪诺夫系统阶梯状空间对照结构解的存在性和形式渐近解的一致有效性. 最后举例验证本文的结果.
英文摘要:
      By means of the first integral method, the author finds a high-dimensional heteroclinic orbit in a fast phase space. He uses the properties of exponential dichotomies and the Fredholm alternatives to determine the internal transition time $t^*$. Using the method of boundary function, he constructs the formal asymptotic solution. Using the method of $k+\sigma$ changing lemma, the existence of a step-type contrast structure for high-dimensional Tikhonov system with boundary conditions is shown and the asymptotic solution is proved to be uniformly effective in the whole interval. Finally, an example is given to demonstrate the effectiveness of the result.
View Full Text  View/Add Comment  Download reader
Close

Organizer:The Ministry of Education of China Sponsor:Fudan University Address:220 Handan Road, Fudan University, Shanghai, China E-mail:edcam@fudan.edu.cn
Designed by Beijing E-Tiller Co.,Ltd.