华东师范大学学报(自然科学版) ›› 2008, Vol. 2008 ›› Issue (5): 72-77,8.

• 应用数学,统计学 • 上一篇    下一篇

奇摄动半线性椭圆型方程的Dirichlet问题

朱振波1,2,倪明康1,2   

  1. 1. 华东师范大学 数学系,上海200062;2. 上海高校计算科学E-研究院 上海交通大学研究所,上海200030
  • 收稿日期:2007-07-07 修回日期:2007-10-22 出版日期:2008-09-25 发布日期:2008-09-25
  • 通讯作者: 倪明康

Dirichlet problem of semi linear singular perturbation elliptic equations(Chinese)

ZHU Zhen-bo1,2, NI Ming-kang1,2

  

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200062,China; 2. Division of Computational Science, E-Institute of Shanghai Universities,SJTU,Shanghai 200030,China
  • Received:2007-07-07 Revised:2007-10-22 Online:2008-09-25 Published:2008-09-25
  • Contact: NI Ming-kang

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摘要： 研究了一类奇摄动半线性椭圆型方程的Dirichlet问题,在M.Vishik和L.Lyusternik坐标变换的基础上,利用边界层函数法构造了其一致有效的渐近解,并进一步构造该问题的上下解, 验证上下解满足Amann条件证明该问题解的存在性, 同时进行了余项估计.

关键词: 奇摄动, 椭圆型方程, 边界层函数, 上下解, 余项估计, 奇摄动, 椭圆型方程, 边界层函数, 上下解, 余项估计

Abstract:

Using transformation of coordinates of M.Vishik and L.Lyusternik, the method of boundary function was used to construct the uniformly valid asymptotic solutions of the Dirichlet problem of semi-linear singular perturbation elliptic equations.Under the uniformly valid asymptotic solutions obtained,the upper and lower solutions were constructed which satisfied the condition of Amann and guranteed the existence of the solution.Finally,the reminder estimation was made.

Key words: elliptic equation, boundary functions, upper and lower solutions, reminder estimation, singular perturbation, elliptic equation, boundary functions, upper and lower solutions, reminder estimation

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