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
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{TMF_2022_212_1_a5,
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--diffusion equations with {Neumann} boundary conditions},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {83--94},
publisher = {mathdoc},
volume = {212},
number = {1},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2022_212_1_a5/}
}
TY - JOUR AU - N. N. Nefedov AU - N. N. Deryugina TI - Existence and stability of a~stable stationary solution with a~boundary layer for a~system of reaction--diffusion equations with Neumann boundary conditions JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2022 SP - 83 EP - 94 VL - 212 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2022_212_1_a5/ LA - ru ID - TMF_2022_212_1_a5 ER -
%0 Journal Article %A N. N. Nefedov %A N. N. Deryugina %T Existence and stability of a~stable stationary solution with a~boundary layer for a~system of reaction--diffusion equations with Neumann boundary conditions %J Teoretičeskaâ i matematičeskaâ fizika %D 2022 %P 83-94 %V 212 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2022_212_1_a5/ %G ru %F TMF_2022_212_1_a5
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/