一类非线性奇摄动方程的激波问题(英文)  

The Shock Problems for a Class of Nonlinear Singularly Perturbed Equations

作　　者：唐荣荣[1] 

机构地区：[1]湖州师范学院数学系,湖州浙江313000

出　　处：《数学进展》2005年第2期233-240,共8页Advances in Mathematics（China）

基　　金：Foundation item: Supported by Important Study Project of the National Natural Science Foundation of China (No. 90211004) and the Natural Science Foundation of Zhejiang (No. 102009).

摘　　要：利用奇摄动理论和匹配原理,讨论了一类非线性奇摄动方程的激波问题.首先,构造了原问题的外部解和内层解.其次,研究了当激波在区间的边界附近和内部的激波解.最后,得出了与边界条件相对应的激波位置及解的表达式.Using the singularly perturbed theory and the matching principle, the shock problems for a class of the nonlinear singularly perturbed equations are considered. Firstly, the outer and internal solutions of the original problem are constructed. Secondly, the shock solutions as the shock layer near the boundary and interior of the interval are studied. Finally, the expressions of the shock solution and shock location relation boundary conditions are obtained.

关 键 词：非线性奇摄动方程 匹配原理 摄动理论 激波位置 边界条件 外部解 原问题 激波解 表达式 内层 区间 

分 类 号：O175.14[理学—数学] TP391.72[理学—基础数学]