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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 9, Pages 1513–1532
DOI: https://doi.org/10.31857/S0044466920090136 (Mi zvmmf11130) 		 
This article is cited in 15 scientific papers (total in 15 papers)

On a periodic inner layer in the reaction–diffusion problem with a modular cubic source

N. N. Nefedov, E. I. Nikulin, A. O. Orlov

Faculty of Physics, Lomonosov Moscow State University, Moscow, 119991 Russia
Citations (15)
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DOI: https://doi.org/10.31857/S0044466920090136
Abstract: The article studies a singularly perturbed periodic problem for the parabolic reaction–diffusion equation in the case of a discontinuous source: a nonlinearity describing the reaction (interaction). The case of the existence of an inner transition layer under conditions of an unbalanced and a balanced reaction is considered. An asymptotic approximation is constructed, and the asymptotic Lyapunov stability of periodic solutions in each of the cases is investigated. To prove the existence of a solution and its asymptotic stability, the asymptotic method of differential inequalities is used. The theoretical result is illustrated by an example and numerical calculations.
Key words: singularly perturbed parabolic problems, periodic problems, reaction–diffusion equations, two-dimensional contrast structures, balanced nonlinearity, inner layers, fronts, asymptotic methods, differential inequalities, asymptotic Lyapunov stability, discontinuous reaction.
Funding agency
This work was supported by the Russian Science Foundation, project no. 18-11-00042.
Received: 11.11.2019
Revised: 10.01.2020
Accepted: 09.04.2020
English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 9, Pages 1461–1479
DOI: https://doi.org/10.1134/S0965542520090134
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: N. N. Nefedov, E. I. Nikulin, A. O. Orlov, “On a periodic inner layer in the reaction–diffusion problem with a modular cubic source”, Zh. Vychisl. Mat. Mat. Fiz., 60:9 (2020), 1513–1532; Comput. Math. Math. Phys., 60:9 (2020), 1461–1479
Citation in format AMSBIB
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