利用衔接法构造奇摄动激波层问题的渐近解  

Constructing Asymptotic Solutions of Singularly Perturbed Shock Layer Problems by Joint Method

作　　者：耿杰 钟家伟 刘树德 GENG JIE;ZHONG JIAWEI;LIU SHUDE(Anhui Institute of Information Technology,Wuhu 241000,China)

机构地区：[1]安徽信息工程学院,芜湖241000

出　　处：《应用数学学报》2022年第3期369-379,共11页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11071005);安徽省高校优秀青年人才支持计划(gxyq2021254);安徽省教学研究(2019jxtd144)资助项目。

摘　　要：研究了一类具有转向点的奇摄动拟线性边值问题,指出在一定条件下解在转向点t=0呈激波层现象.先用合成展开法构造出问题的形式近似,然后利用衔接法将t=0左、右两边分别具有边界层性质的近似式光滑地衔接起来,从而形成在t=0处具有激波层性质的解,并应用微分不等式理论证明了解的存在性及其渐近性质.Some singularly perturbed quasilinear boundary value problems are studied.Under certain conditions,solutions are shown to exhibit shock layer behavior at turning point t=0.The formal approximation of problems is constructed using the method of composite expansions,and then approximation solutions of left and right sides at t= 0 are jointed by joint method which exhibits boundary layer behavior respectively.As a result a approximate solution which exhibits shock layer behavior at t=0 is formed.And the existence and asymptotic behavior of solutions are proved by the theory of differential inequalities.

关 键 词：奇摄动 拟线性边值问题 激波层 衔接法 合成展开法 微分不等式 

分 类 号：O175.14[理学—数学]