具有两参数的椭圆型方程Robin问题解的渐近性态

具有两参数的椭圆型方程Robin问题解的渐近性态 Asymptotic Behavior of Solution for the Robin Problem of Elliptic Equation with Two Parameters 莫嘉琪 MO Jiaqi1 1 2 3 4 5 first-author 陈丽华 CHEN Lihua3 1 2 3 4 5 安徽师范大学数学系 安徽师范大学数学系 Department of Mathematics,Anhui Normal University Department of Mathematics,Anhui Normal University 福建师范大学福清分校数学与计算机科学系,安徽,芜湖,241000 福建师范大学福清分校数学与计算机科学系,安徽,芜湖,241000 Division of Computational Science,E-Institutes of Shanghai Universities at Shanghai Jiao Tong University Division of Computational Science,E-Institutes of Shanghai Universities at Shanghai Jiao Tong University 上海高校计算科学E-研究院上海交通大学研究所 上海高校计算科学E-研究院上海交通大学研究所 Department of Mathematics and Computer Science,Fuqing Branch of Fujian Normal University,Fuqing Department of Mathematics and Computer Science,Fuqing Branch of Fujian Normal University,Fuqing ,上海,200240 ,上海,200240 福建福清,350300 福建福清,350300 讨论了一类具有双参数的椭圆型方程边值问题.引入伸长变量,构造了问题的形式渐近解.利用微分不等式理论,证明了边值问题渐近解的存在性和一致有效性.由解的结构指出,在两参数一定的情况下,相应问题的解只具有二个边界层. A class of boundary value problem for elliptic equation with two parameters is considered.Introducing a stretched variable,the formal asymptotic solution is constructed.By using the theory of differential inequalities,the existence and uniform validity of the asymptotic solution for boundary value problem are proved.The structure of the solution also suggests that the solution of corresponding problem has two boundary layers under suitable conditions for two parameters. 非线性 两参数 奇摄动 nonlinear two parameters singular perturbation O175.25 国家自然科学基金资助项目（40676016,10471039）;国家重点基础研究发展规划（973）项目（2003CB415101-03,2004CB418304）;中国科学院知识创新工程方向性项目（KZCX3-SW-221）;上海市教育委员会E-研究院建设计划项目（E03004） 2008-03-01 2021-04-01 3