两参数非线性椭圆型方程的激波渐近解（英文）  

The Shock Asympototic Solution for Nonlinear Elliptic Equation with Two Parameters

作　　者：冯依虎[1] 莫嘉琪[2] 

机构地区：[1]亳州师范高等专科学校电子与信息工程系,安徽亳州236800 [2]安徽师范大学数学系,安徽芜湖241003

出　　处：《应用数学》2015年第3期579-585,共7页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11202106);the Natural Science Foundation of the Education Department of Anhui Province,China(KJ2013B153)

摘　　要：本文讨论一类两参数非线性椭圆型方程边值问题.得到原问题的外部解,引入伸长变量和在边界和外部解的内部间断点附近设置局部坐标系,构造边界层和内部层校正项.在适当的条件下,利用微分不等式,证明边值问题激波解的存在性并研究解的渐近性态.The boundary value problem for the nonlinear elliptic equation with two parameters is considered. The outer solution for the original problem is obtained. Introducing stretched variables and setting local coordinate systems near the boundary and interior discontinuous point of outer solution construct the boundary and interior layer correetion terms. Under suitable conditions, using the differential inequalities the existence of the shock solution for boundary value problem is proved and the asymptotic behavior of the solution is studied.

关 键 词：激波 椭圆性方程 渐近解 

分 类 号：O175.29[理学—数学]