| 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. |
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| 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. |
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