一类两参数奇异摄动拟线性微分方程组的边值问题渐近解  

Asymptotic Solutions to a Class of the Quasilinear System of Differential Equations with Two Parameters and Boundary Value Conditions

作　　者：葛志新[1] 

机构地区：[1]安徽工业大学数理学院,马鞍山243002

出　　处：《工程数学学报》2013年第4期611-618,共8页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10371006)~~

摘　　要：为了研究一类含三个因变量的两参数奇异摄动拟线性微分方程组边值问题的渐近解,首先在一定的条件下构造了问题的包含外层解、中间层解与内部层解的幂级数形式合成解;然后利用原问题的退化形式先求出外部解;再利用不同的伸长变量,依据中间层与内部层特有的性质,分别计算出该边值问题的中间层解和内部层解,从而得到原问题渐近解.In order to study the asymptotic solutions to a class of the quasilinear system of differential equations containing three dependent variables with two parameters and boundary value conditions, firstly the power series expansion consisting of the outer layer solution, the middle layer solution and interior layer solution are formulated under certain conditions. Then the outer layer solution is obtained by the degenerate problem of the original problem. Finally by utilizing various stretched variables, based on the nature of the middle layer and interior layer, the middle layer solution and the interior solution are given respectively. The asymptotic solution to the class of the auasilinear system of equations is thus obtained.

关 键 词：奇摄动 拟线性微分方程组 两参数 

分 类 号：O175.14[理学—数学]