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Periodic Contrast Structures in the Reaction-Diffusion Problem with Fast Response and Weak Diffusion

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Abstract

In this paper, we study a new class of time-periodic solutions with interior transition layer of reaction-advection-diffusion equations in the case of a fast reaction and a small diffusion. We consider the case of discontinuous sources (i.e., the nonlinearity describing the interaction and reaction) for a certain value of the unknown function that arise in a number of relevant applications. An existence theorem is proved, asymptotic approximations are constructed, and the asymptotic Lyapunov stability of such solutions as solutions of the corresponding initial-boundary-value problems is established.

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Funding

This work was supported by the Russian Science Foundation under grant 18-11-00042.

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Authors and Affiliations

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

    N. N. Nefedov

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  1. N. N. Nefedov
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Correspondence to N. N. Nefedov.

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Translated from Matematicheskie Zametki, 2022, Vol. 112, pp. 601–612 https://doi.org/10.4213/mzm13732.

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Nefedov, N.N. Periodic Contrast Structures in the Reaction-Diffusion Problem with Fast Response and Weak Diffusion. Math Notes 112, 588–597 (2022). https://doi.org/10.1134/S0001434622090279

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  • DOI: https://doi.org/10.1134/S0001434622090279

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