具有两个转向点的奇摄动边界层和内角层问题  

Singularly perturbed boundary and interior corner layer problems with two turning points

作　　者：凌婷婷 刘树德 丁伯伦 

机构地区：[1]安徽信息工程学院,安徽芜湖241000

出　　处：《应用数学与计算数学学报》2017年第3期385-391,共7页Communication on Applied Mathematics and Computation

基　　金：安徽省自然科学基金资助项目(KJ2017A792)

摘　　要：在方程的一阶导数项的系数有两个零点,即方程有两个转向点的主要假设下研究了一类奇摄动二阶线性边值问题,先分析在边界点和转向点处可能出现层现象的条件,再通过外展开式构造外部解、内展开式构造边界层或内角层,利用匹配渐近展开法,包括使用Prandtl匹配原则、Van Dyke匹配原则及中间变量匹配原则,将内展开式与外部解进行匹配,从而得到在相应区间上一致有效的复合展开式.Some singularly perturbed second order linear boundary value prob- lems are studied under the principal assumption that the coefficient of the first derivative term in the equation has two zero points, i.e., this equation has two turning points. Layer phenomena which may be occurring at bounding and turn- ing points are analyzed. An outer solution, and at the same time, a boundary layer and an inner corner layer are constructed by outer expansion and inner ex- pansion. A composite expansion that is uniformly valid over the corresponding interval is obtained using the method of matched asymptotic expansions includ- ing Prandtl matching principle, Van Dyke matching principle and the immediate variable matching principle.

关 键 词：奇摄动 边值问题 转向点 角层 匹配渐近展开法 

分 类 号：O175.8[理学—数学]