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高校应用数学学报
高校应用数学学报  2015, Vol. 30 Issue (1): 117-126    
    
一个奇摄动微分方程非线性混合边值问题
陈雯, 姚静荪, 孙国正
安徽师范大学 数学计算机科学学院, 安徽芜湖 241003
A nonlinear mixed boundary value problem for singularly perturbed differential equation
CHEN Wen, YAO Jing-sun, SUN Guo-zheng
College of Mathematics and computer science, Anhui Normal University, Wuhu 241003, China
 全文: PDF 
摘要： 研究了一个三阶半线性微分方程的奇摄动非线性混合边值问题. 利用边界层函数法构造了该问题的形式渐近解, 并采用微分不等式理论证明了解的存在性, 给出了渐近解的误差估计, 最后得出了边界层函数指数型衰减的结论.
关键词： 奇摄动;  三阶微分方程;  边界层函数法;  指数型衰减;  微分不等式理论    
Abstract: In this paper, a singularly perturbed nonlinear mixed boundary value problem for third-order semilinear differential equation is studied. The formal asymptotic solution to this problem is constructed by the method of boundary layer functions. According to the theory of differential inequalities, the existence of solution is proved and the error estimate of asymptotic solution is given. Finally, the exponential decay of boundary layer functions for this problem is concluded.
Key words: singular perturbation    third-order differential equation    boundary layer function method    exponential decay    the theory of differential inequality
收稿日期: 2014-10-07 出版日期: 2018-06-06
CLC:  O175.14  
基金资助: 国家自然科学基金(11271020)
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陈雯
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引用本文:

陈雯, 姚静荪, 孙国正. 一个奇摄动微分方程非线性混合边值问题[J]. 高校应用数学学报, 2015, 30(1): 117-126.

CHEN Wen, YAO Jing-sun, SUN Guo-zheng. A nonlinear mixed boundary value problem for singularly perturbed differential equation. Applied Mathematics A Journal of Chinese Universities, 2015, 30(1): 117-126.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2015/V30/I1/117

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