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Contrast Structures in the Reaction-Diffusion-Advection Problem in the Case of a Weak Reaction Discontinuity

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Abstract

In the paper, a boundary value problem for a singularly perturbed equation of reaction-diffusion-advection in a two-dimensional domain is considered. The key feature of the problem under consideration is the weak discontinuity of the reactive term. The discontinuity occurs on a simple closed curve known in advance that lies entirely inside the domain. It is shown that such a problem has a solution with an inner transition layer localized near the discontinuity curve. For this solution, an asymptotic expansion with respect to a small parameter is constructed, and existence theorems are proved, together with Lyapunov asymptotic stability. As a method of the proof, the asymptotic method of differential inequalities is used. An example is given illustrating the constructions carried out in the paper.

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Funding

This work was supported by a grant from the Russian Science Foundation no. 21-71-00070.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    N. N. Nefedov, E. I. Nikulin & A. O. Orlov

Authors
  1. N. N. Nefedov
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  2. E. I. Nikulin
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  3. A. O. Orlov
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Correspondence to N. N. Nefedov or E. I. Nikulin.

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Nefedov, N.N., Nikulin, E.I. & Orlov, A.O. Contrast Structures in the Reaction-Diffusion-Advection Problem in the Case of a Weak Reaction Discontinuity. Russ. J. Math. Phys. 29, 81–90 (2022). https://doi.org/10.1134/S1061920822010083

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