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Multizonal Boundary and Internal Layers in the Singularly Perturbed Problems for a Stationary Equation of Reaction–Advection–Diffusion Type with Weak and Discontinuous Nonlinearity

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Abstract

A singularly perturbed Dirichlet boundary value problem for a stationary equation of reaction–advection–diffusion type with multiple roots of the degenerate equation is studied. This is a new class of problems with discontinuous reactive and weak advective terms. The existence of a contrast structure solution is proved by using the method of asymptotic differential inequalities and matching asymptotic expansion. And we show that the multiple roots lead to the formation of multizonal boundary and internal layers in the neighborhood of the boundary and the discontinuity point, which is essentially quite different from the case of isolated roots.

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ACKNOWLEDGMENTS

This work is supported by the National Natural Science Foundation of China (no. 11871217) and the Science and Technology Commission of Shanghai Municipality (no. 18dz2271000). The corresponding author is Mingkang Ni.

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Authors and Affiliations

  1. College of Science, University of Shanghai for Science and Technology, 200093, Shanghai, China

    Q. Yang

  2. School of Mathematical Sciences, East China Normal University, 200062, Shanghai, China

    Mingkang Ni

  3. Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, 200062, Shanghai, China

    Mingkang Ni

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  1. Q. Yang
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  2. Mingkang Ni
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Correspondence to Q. Yang or Mingkang Ni.

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Yang, Q., Ni, M. Multizonal Boundary and Internal Layers in the Singularly Perturbed Problems for a Stationary Equation of Reaction–Advection–Diffusion Type with Weak and Discontinuous Nonlinearity. Comput. Math. and Math. Phys. 62, 2123–2138 (2022). https://doi.org/10.1134/S0965542522120144

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  • DOI: https://doi.org/10.1134/S0965542522120144

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