一个奇摄动微分方程非线性混合边值问题  

A nonlinear mixed boundary value problem for singularly perturbed differential equation

作　　者：陈雯[1] 姚静荪[1] 孙国正[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241003

出　　处：《高校应用数学学报（A辑）》2015年第1期117-126,共10页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11271020)

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.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.

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 

分 类 号：O175.14[理学—数学]