数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (2): 793-799.doi: 10.1016/S0252-9602(12)60059-9

• 论文 • 上一篇    下一篇

SINGULARLY PERTURBED SEMI-LINEAR BOUNDARY VALUE PROBLEM WITH DISCONTINUOUS FUNCTION

丁海云1,2|倪明康1,3|林武忠1,3|曹扬4   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200241, China
    2. Department of Mathematics, Shanghai Maritime University, Shanghai 200135, China
    3. Division of Computational Science,E-institute of Shanghai Jiaotong University, Shanghai 200030, China|4.School of Economics &|Management, Shanghai Institute of Technology, Shanghai 201418, China
  • 收稿日期:2010-03-16 出版日期:2012-03-20 发布日期:2012-03-20
  • 基金资助:

    Supported by National Natural Science Foundation of China (11071075, 11171113), National Natural Science Foundation of China-subsidized by CAS Knowledge Innovation Project (30921064, 90820307), Shang Natural Science Foundation (10ZR1409200), and Division of Computational Sci-ence, E-institute of Shanghai Jiaotong University(E03004).

SINGULARLY PERTURBED SEMI-LINEAR BOUNDARY VALUE PROBLEM WITH DISCONTINUOUS FUNCTION

 DING Hai-Yun1,2, NI Ming-Kang1,3, LIN Wu-Zhong1,3, CAO Yang4   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200241, China
    2. Department of Mathematics, Shanghai Maritime University, Shanghai 200135, China
    3. Division of Computational Science,E-institute of Shanghai Jiaotong University, Shanghai 200030, China|4.School of Economics &|Management, Shanghai Institute of Technology, Shanghai 201418, China
  • Received:2010-03-16 Online:2012-03-20 Published:2012-03-20
  • Supported by:

    Supported by National Natural Science Foundation of China (11071075, 11171113), National Natural Science Foundation of China-subsidized by CAS Knowledge Innovation Project (30921064, 90820307), Shang Natural Science Foundation (10ZR1409200), and Division of Computational Sci-ence, E-institute of Shanghai Jiaotong University(E03004).

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摘要：

A class of singularly perturbed semi-linear boundary value problems with discontinuous functions is examined in this article. Using the boundary layer function method, the asymptotic solution of such a problem is given and shown to be uniformly effective. The existence and uniqueness of the solution for the system is also proved. Numerical result is presented as an illustration to the theoretical result.

关键词: Singular perturbation, asymptotic expansion, boundary layer function, in-variant manifold

Abstract:

A class of singularly perturbed semi-linear boundary value problems with discontinuous functions is examined in this article. Using the boundary layer function method, the asymptotic solution of such a problem is given and shown to be uniformly effective. The existence and uniqueness of the solution for the system is also proved. Numerical result is presented as an illustration to the theoretical result.

Key words: Singular perturbation, asymptotic expansion, boundary layer function, in-variant manifold

中图分类号: 

  • 34B16
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