摘要
利用匹配渐近展开法,研究了一类带参数的非线性奇摄动边值问题.首先找到满足退化方程的外部解,然后根据参数k的变化分五种情况找到用特殊函数表示的内层解,得到了该问题具有左边界层、右边界层或内部层之一的结论(其中左、右边界层又各分为两种情况).最后通过匹配原则,将内外展开式进行匹配给出了该问题的一致有效的零阶渐近展开式.
A class of nonlinear singularly perturbed problems with parameter is discussed using the matching asymptotic expanding method. Firstly, the outer solutions to satisfy the degenerate equation are found. The inner solutions expressed with special function are gotten as the five different cases of parameter, then theconclusion that the problem must have one of the boundary layers at left, right and interior （where the left boundary layer has two different cases and also the right） is obtained. Finally, zero-order uniformly valid asymptotic expansions of the problem are given by matching the outer and inner solutions according to the matching principle.
出处
《安徽师范大学学报（自然科学版）》
CAS
北大核心
2012年第1期16-20,共5页
Journal of Anhui Normal University(Natural Science)
基金
国家自然科学基金项目(11071205
10902076)
浙江省自然科学基金项目(Y6110502)
浙江省精品课程<常微分方程>
关键词
非线性
奇摄动
边界层
匹配
渐近解
nonlinear
singular perturbation
boundary layer
matching
asymptotic solution
