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Asymptotic Analysis for the Singularly Perturbed Initial Value Problem with Degenerate Equation Having Triple Root

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Abstract

In this paper, we study the asymptotic behavior of the initial value problem for the singularly perturbed first order nonlinear differential equation with degenerate equation having triple root. In order to obtain a more precise description of the boundary layer, the modified method of boundary layer function is chosen to construct the boundary layer function possessing the behavior of exponential decay characteristic, and then the asymptotic solution is constructed and used to prove that the formal asymptotic solution is uniformly valids.

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Acknowledgements

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Authors and Affiliations

  1. School of Mathematics and Physics, Anhui University of Technology, Maanshan City, 243002, Anhui Province, China

    Songlin Chen & Ruirui Zhang

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  1. Songlin Chen
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  2. Ruirui Zhang
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Correspondence to Songlin Chen.

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This work was completed with the support of our -pert.

Supported by the Natural Science Research Major Project from Universities of Anhui Province (Grant No. KJ2016A084) and the Postgraduate Innovation Foundation of Anhui University of Technology (Grant No. 2014131).

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Chen, S., Zhang, R. Asymptotic Analysis for the Singularly Perturbed Initial Value Problem with Degenerate Equation Having Triple Root. Qual. Theory Dyn. Syst. 17, 91–101 (2018). https://doi.org/10.1007/s12346-017-0234-3

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  • DOI: https://doi.org/10.1007/s12346-017-0234-3

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