一类含有双边界层的二次奇摄动边值问题  

A CLASS OF THE QUADRATIC SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS WITH TWOFOLD BOUNDARY LAYER

作　　者：许进 Xu Jin(Department of Basic Courses,Wentian College of Hohai University,Ma5anshan 243031)

机构地区：[1]河海大学文天学院基础部

出　　处：《南京大学学报（数学半年刊）》2019年第1期100-107,共8页Journal of Nanjing University(Mathematical Biquarterly)

基　　金：河海大学文天学院校级自然科学基金资助课题(WT2016032)

摘　　要：本文研究了一类含有双边界层的二次奇摄动边值问题.在适当的条件下,用合成展开法构造出该问题的形式近似式,并应用二阶微分不等式理论证明解的存在性,最后通过构造界定函数给出解的渐近估计.In this paper,a class of the quadratic singularly perturbed boundary value problems with twofold boundary layer is studied.Under the appropriate conditions,the formal approximation of the problems is constructed by using the method of composite expansions,and the existence of the solution is proved by the theory of second order differential inequalities.At last,the asymptotic estimation of the solution is given by constructing the defined functions.

关 键 词：二次奇摄动 边界层 边值问题 界定函数 合成展开法 微分不等式理论 

分 类 号：O175.8[理学—数学]