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Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (5): 655-666.doi: https://doi.org/10.1007/s10483-014-1819-7

• 论文 • 上一篇    

Contrast structure for singular singularly perturbed boundary value problem

王爱峰1 倪明康2   

  1. 1. School of Mathematical Science, Huaiyin Normal University, Huaian 223001, Jiangsu Province, P. R. China;
    2. Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China
  • 收稿日期:2013-08-27 修回日期:2013-11-16 出版日期:2014-05-01 发布日期:2014-05-01

Contrast structure for singular singularly perturbed boundary value problem

WANG Ai-Feng1, NI Ming-Kang2   

  1. 1. School of Mathematical Science, Huaiyin Normal University, Huaian 223001, Jiangsu Province, P. R. China;
    2. Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China
  • Received:2013-08-27 Revised:2013-11-16 Online:2014-05-01 Published:2014-05-01

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摘要： The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit smooth, the existence of the steptype solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of the present results.

关键词: contrast structure, singular singularly perturbation, asymptotic expansion, boundary function

Abstract: The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit smooth, the existence of the steptype solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of the present results.

Key words: contrast structure, singular singularly perturbation, asymptotic expansion, boundary function

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