几类具有奇性的奇摄动方程的初边值问题的渐近性态
Asymptotic Behaviors for Some Initial Boundary Value Problems of Singularly Perturbed Equation Possessing Singularity
DOI: 10.12677/AAM.2020.94057, PDF,   
作者: 杜亚洁, 陈松林：安徽工业大学，数理科学与工程学院，安徽 马鞍山
关键词: 奇摄动问题；重边界层；匹配法；奇性；一致有效性；Singularly Perturbed Problem； Double Layer； Matching Method； Singularity； Uniformly Valid
摘要: 本文研究了两类具有奇性的奇摄动初边值问题，研究结果表明此类问题具有重边界层现象。利用匹配渐近展开法构造出了问题的形式渐近解，同时，用微分不等式理论证明了渐近解的一致有效性。
Abstract: In this paper, two types of singularly perturbed initial boundary value problems with singularity are studied. The research results show that this type of problem has a double-layer phenomenon. The asymptotic solutions of the equation are constructed by the matched asymptotic expansion method, and the uniform validity of the asymptotic solutions is proved by the differential inequality theory.
文章引用：杜亚洁, 陈松林. 几类具有奇性的奇摄动方程的初边值问题的渐近性态[J]. 应用数学进展, 2020, 9(4): 467-477. https://doi.org/10.12677/AAM.2020.94057

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