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Internal Transition Layer Structure in the Reaction–Diffusion Problem for the Case of a Balanced Reaction with a Weak Discontinuity

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Abstract

For a singularly perturbed reaction–diffusion equation, we study the structure of the internal transition layer in the case of a balanced reaction with a weak discontinuity. The existence of solutions with an internal transition layer (contrast structures) is proved, the question of their stability is investigated, and asymptotic approximations to solutions of this type are obtained. It is shown that in the case of reaction balance, the presence of even a weak (asymptotically small) reaction discontinuity can lead to the formation of contrast structures of finite size, both stable and unstable.

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Funding

This work was financially supported by the Russian Science Foundation, project no. 23-11-00069.

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Authors and Affiliations

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

    E. I. Nikulin, V. T. Volkov & D. A. Karmanov

Authors
  1. E. I. Nikulin
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  2. V. T. Volkov
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  3. D. A. Karmanov
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Corresponding authors

Correspondence to E. I. Nikulin, V. T. Volkov or D. A. Karmanov.

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Translated by V. Potapchouck

CONFLICT OF INTEREST. The authors of this work declare that they have no conflicts of interest.

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Nikulin, E.I., Volkov, V.T. & Karmanov, D.A. Internal Transition Layer Structure in the Reaction–Diffusion Problem for the Case of a Balanced Reaction with a Weak Discontinuity. Diff Equat 60, 65–76 (2024). https://doi.org/10.1134/S0012266124010063

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  • DOI: https://doi.org/10.1134/S0012266124010063

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