一类非线性奇摄动问题边界层与边值的关系  

The Relation Between Boundary Layer and Boundary-value for A Class of Nonlinear Singularly Perturbed Problem

作　　者：周倩[1] 陈松林[1] 

机构地区：[1]安徽工业大学数理学院,安徽马鞍山243032

出　　处：《合肥学院学报（自然科学版）》2011年第4期12-15,共4页Journal of Hefei University :Natural Sciences

基　　金：国家自然基金项目(41075027D0503);科技部创新方法专项子项目(2009IM010400)资助

摘　　要：利用匹配渐近展开法,讨论了一类二阶非线性奇摄动问题εy″+yy'+xy+y2=0,x∈(0,1),y(0)=α,y(1)=β,通过匹配方程的内层解、外部解及边界层解,得出解的层性态与边界条件的关系,并给出了解的渐近表示.The solution for a class of nonlinear singularly perturbed equation of second-order εy″＋yy′＋xy＋y^2=0,x∈（0,1）,y（0）=α,y（1）=β is considered by using the method of matched asymptotic expansion.The relation between the layer＇s quality of its solution and its boundary conditions is discussed by matching interior solution,outer solution and boundary solutions of the problem.And the asymptotic expansion of solution is obtained.

关 键 词：非线性方程 边界层 内部层 匹配渐近展开 

分 类 号：O175.14[理学—数学]