利用匹配法构造一类燃烧问题的角层近似解  

Approximate Solutions to Corner Layer for a Class of Combustion Problem with the Method of Matched Asymptotic Expansions

作　　者：黄飞 刘树德 Huang Fei;Liu Shude(School of General Education and Foreign Languages,Anhui Institute of Information Technology,Wuhu 241000,China;College of Mathematics and Computer Science,Anhui Normal University,Wuhu 241000,China)

机构地区：[1]安徽信息工程学院通识教育与外国语学院,安徽芜湖241000 [2]安徽师范大学数学与统计学院,安徽芜湖241000

出　　处：《黄山学院学报》2021年第5期5-7,共3页Journal of Huangshan University

基　　金：安徽省教育厅自然科学研究重点项目(KJ2019A1289);安徽省一流教材建设项目(2018yljc146);安徽省高校优秀人才支持计划项目(gxyq2020105)。

摘　　要：研究了一类出现在燃烧理论中的奇摄动边值问题。利用匹配渐近展开法先确定内角层的位置,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零次近似解。A class of singularly perturbed boundary value problem arising in theory of combustion is studied.The location of an inner corner layer is determined and the inner and outer expansion with different scales are developed by using the method of matched asymptotic expansions.Then,a composite expansion that is uniformly valid over the whole interval is constructed by equating the inner limit of the outer expansion and the outer limit of inner expansion according to the matching principle.Thus,a zero-order approximate solution to the problem is obtained with corner layer properties.

关 键 词：燃烧问题 奇摄动 角层 近似解 匹配渐近展开法 

分 类 号：O175.14[理学—数学]