一类二次奇摄动问题的角层近似解的构造  

Construction of Approximate Solutions with Corner layer for Some Quadratic Singular Perturbation Problems

作　　者：钟家伟 凌婷婷 刘树德 ZHONG Jia-wei;LING Ting-ting;LIU Shu-de(Anhui Institute of Information Technology,Wuhu 241000,Anhui,China)

机构地区：[1]安徽信息工程学院,安徽芜湖241000

出　　处：《合肥学院学报（综合版）》2021年第5期20-23,共4页Journal of Hefei University：Comprehensive ED

基　　金：安徽省高校自然科学重点项目“有限环上的常循环码及其量子码的构造方法研究”(KJ2019A1286);“偏微分方程在图像分割中的应用研究”(KJ2019A1297)资助。

摘　　要：研究了一类二次奇摄动问题。利用匹配渐近展开法求出两个不同尺度的内、外展开式,然后按匹配原则进行匹配,使外展开式的内极限等于内展开式的外极限,形成在整个区间上一致有效的复合展开式,从而得到该问题具有角层性质的近似解。Some quadratic singular perturbation problems are considered.The inner and outer expansion with different scales are developed using the method of matched asymptotic expansions.Then,a composite expansion that is uniformly valid over the whole interval is constructed equating the inner limit of the outer expansion and the outer limit of inner expansion according to the matching principle.Thus,an approximate solution of the problem is obtained which exhibits corner layer behavior.

关 键 词：奇摄动 二次边值问题 角层 近似解 匹配渐近展开法 

分 类 号：O175.14[理学—数学]