Abstract
We consider an initial boundary value problem for a singularly perturbed parabolic system of two reaction–diffusion-type equations with Neumann conditions, where the diffusion coefficients are of different degrees of smallness and the right-hand sides need not be quasimonotonic. We obtain an asymptotic approximation of the stationary solution with a boundary layer and prove existence theorems, the asymptotic stability in the sense of Lyapunov, and the local uniqueness of such a solution. The obtained result is applied to a class of problems of chemical kinetics.
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This paper is supported by the Russian Science Foundation grant No. 18-11-00042.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2022, Vol. 212, pp. 83–94 https://doi.org/10.4213/tmf10255.
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Nefedov, N.N., Deryugina, N.N. Existence and stability of a stable stationary solution with a boundary layer for a system of reaction–diffusion equations with Neumann boundary conditions. Theor Math Phys 212, 962–971 (2022). https://doi.org/10.1134/S0040577922070066
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DOI: https://doi.org/10.1134/S0040577922070066