两类具有激波层性态的奇摄动边值问题  

Two kinds of singularly perturbed boundary value problems with shock layer properties

作　　者：马晴晴 张志明 MA Qingqing;ZHANG Zhiming(School of Mathematics and Statistics,Fuyang Normal University,Fuyang Anhui 236037,China)

机构地区：[1]阜阳师范大学数学与统计学院,安徽阜阳236037

出　　处：《阜阳师范大学学报（自然科学版）》2021年第2期21-25,共5页Journal of Fuyang Normal University:Natural Science

基　　金：安徽省自然科学基金项目(1908085MF192)资助。

摘　　要：文章研究了两类具有激波层特质的奇摄动边值问题。讨论了一类拟线性和一类二次边值问题的激波层性态,在适当条件下,利用合成展开法分析出激波层校正项,通过衔接法形成复合展开式,从而构造出内外解,应用微分不等式的理论较简捷地证明了解的存在性。This paper studies two types of singularly perturbed boundary value problems with shock layer characteristics.The shock layer behavior of a class of quasi-linear and a class of quadratic boundary value problems were discussed.Under appropriate conditions,the synthetic expansion method was used to analyze the shock layer correction term,and form the compound expansion by the connection method to construct the inner and outer solutions,apply the theory of differential inequality to prove its existence more concisely.

关 键 词：奇摄动 激波层 内层问题 合成展开发 衔接法 

分 类 号：O175.8[理学—数学]