Geodesic
Existence and stability of a stable stationary solution with a boundary layer for a system of reaction–diffusion equations with Neumann boundary conditions
Teoretičeskaâ i matematičeskaâ fizika, Tome 212 (2022) no. 1, pp. 83-94 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {N. N. Nefedov and N. N. Deryugina},
     title = {Existence and stability of a~stable stationary solution with a~boundary layer for a~system of reaction{\textendash}diffusion equations with {Neumann} boundary conditions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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N. N. Nefedov; N. N. Deryugina. Existence and stability of a stable stationary solution with a boundary layer for a system of reaction–diffusion equations with Neumann boundary conditions. Teoretičeskaâ i matematičeskaâ fizika, Tome 212 (2022) no. 1, pp. 83-94. http://geodesic.mathdoc.fr/item/TMF_2022_212_1_a5/

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