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Internal Layer for a System of Singularly Perturbed Equations with Discontinuous Right-Hand Side

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Abstract

We study a system of two singularly perturbed first-order equations on an interval. The equations have discontinuous right-hand sides and equal powers of the small parameter multiplying the derivatives. We consider a new class of problems with discontinuous right-hand side, prove the existence of a solution with an internal transition layer, and construct its asymptotic approximation of arbitrary order. The asymptotic approximations are constructed by the Vasil’eva method, and the existence theorems are proved by the matching method.

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Authors and Affiliations

  1. Institute for Mathematics and Statistics at Anhui Normal University, Wuhu, China

    Pang Yafei

  2. Institute for Mathematical Sciences at East China Normal University, Shanghai, China

    Ni Mingkang

  3. Lomonosov Moscow State University, Moscow, 119991, Russia

    N. T. Levashova

Authors
  1. Pang Yafei
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  2. Ni Mingkang
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  3. N. T. Levashova
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Corresponding author

Correspondence to Ni Mingkang.

Additional information

Original Russian Text © Pang Yafei, Ni Mingkang, N.T. Levashova, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 12, pp. 1626–1637.

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Yafei, P., Mingkang, N. & Levashova, N.T. Internal Layer for a System of Singularly Perturbed Equations with Discontinuous Right-Hand Side. Diff Equat 54, 1583–1594 (2018). https://doi.org/10.1134/S0012266118120054

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  • DOI: https://doi.org/10.1134/S0012266118120054

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