摘要
利用匹配渐近展开法,讨论一类非线性奇摄动边值问题中边界层内存在两个特异极限的多层解.首先,构造原问题的外部解;其次,利用伸长变量,求得了两个特异极限,进而得到了对应问题的两个内部解;最后,研究了边界层位于三种不同位置的多层解,利用匹配原则,求出了各种情形解的一致有效的零次渐近展开式。并解决了一类特殊的转向点问题。
By using the matching asymptotic expanding method,the multi-layer solution with two special limits in boundary layer for a class of nonlinear singularly perturbed boundary value problems is discussed.Firstly,the outer of the original problem is constructed.Secondly,by using the stretched variable,two special limits are equated and the two inner solutions to the corresponding problem are obtained further.Finally,the multi-layer solutions are studied for boundary layer located three different locations,and using the matching principle,uniformly valid zero order asymptotic expansion is obtained.And a class of particular turning point problems is solved.
出处
《南昌大学学报（理科版）》
CAS
北大核心
2010年第6期523-526,共4页
Journal of Nanchang University(Natural Science)
基金
国家自然科学基金资助项目(11071205)
国家特色专业(数学与应用数学)
浙江省新世纪教改基金资助项目(YB07109
ZC09063)
湖州师范学院重点教改基金资助项目(GJB09004)
常微分方程精品课程资助
关键词
非线性
奇摄动
匹配
多层
边界层
nonlinear
singular perturbation
matching
multi-layer
boundary layer
