This article is cited in 4 papers

Existence and stability of a stable stationary solution with a boundary layer for a system of reaction–diffusion equations with Neumann boundary conditions

N. N. Nefedov, N. N. Deryugina

Physical Faculty, Lomonosov Moscow State University, Moscow, Russia

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.

Keywords: reaction–diffusion systems, stationary solution, quasimonotonicity conditions, method of differential inequalities, upper and lower solutions, boundary layer, stability in the sense of Lyapunov.

Received: 21.01.2022
Revised: 21.01.2022

DOI: 10.4213/tmf10255

 English version: Theoretical and Mathematical Physics, 2022, 212:1, 962–971

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