Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (4): 865-874.

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The Contrast Structure for the Singularly Perturbed Problem with Slow-Fast Layers and Discontinuous Righthand Side

Huaxiong Chen1,*(),Yanyan Wang1,Mingkang Ni2   

  1. 1 School of Mathematics and Statistics, Zhoukou Normal University, Henan Zhoukou 466000
    2 School of Mathematical Sciences, East China Normal University, Shanghai 200241
  • Received:2017-12-12 Online:2019-08-26 Published:2019-09-11
  • Contact: Huaxiong Chen
  • Supported by:
    the NSFC(61703447);the Key Research Projects in University of Henan Province(19A110038);the Key Research Projects in University of Henan Province(18A110039);the Research Fund Projects of Zhoukou Normal University(ZKNUC2016012);the Research Fund Projects of Zhoukou Normal University(ZKNUC2017020);the Research Fund Projects of Zhoukou Normal University(ZKNUB2201806)


This paper discusses the contrast structure solution for the singularly perturbed problem with slow-fast layers and discontinuous righthand side. By applying the boundary function method, the asymptotic solution of this problem is constructed. Then using the sewing connection method, the existence of the solution is shown and the asymptotic solution is proved to be uniformly valid. Finally, an example is given to illustrate the main results.

Key words: Singular perturbation, Contrast structure, Boundary layer function method, Sewing connection method

CLC Number: 

  • O29