Geodesic
Existence, Asymptotics, and Lyapunov Stability of Solutions of Periodic Parabolic Problems for Tikhonov-Type Reaction--Diffusion Systems
Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 276-285

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We study a new class of time-periodic solutions of singularly perturbed systems of reaction–diffusion equations in the case of a fast and a slow equation, which are usually called Tikhonov-type systems. A boundary layer asymptotics of solutions is constructed, the existence of solutions with this asymptotics is proved, and conditions for the Lyapunov asymptotic stability of these solutions treated as solutions of the corresponding initial–boudary value problems are obtained.
Keywords: singularly perturbed problem, periodic parabolic boundary value problem, boundary and interior layers, asymptotic expansion, differential inequality, Lyapunov stability.
Mots-clés : reaction–diffusion equations 
@article{MZM_2024_115_2_a10,
     author = {N. N. Nefedov},
     title = {Existence, {Asymptotics,} and {Lyapunov} {Stability} of {Solutions} of {Periodic} {Parabolic} {Problems} for {Tikhonov-Type} {Reaction--Diffusion} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {276--285},
     publisher = {mathdoc},
     volume = {115},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a10/}
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N. N. Nefedov. Existence, Asymptotics, and Lyapunov Stability of Solutions of Periodic Parabolic Problems for Tikhonov-Type Reaction--Diffusion Systems. Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 276-285. http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a10/