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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 10, Page 1695
DOI: https://doi.org/10.31857/S0044466922100118 (Mi zvmmf11461) 		 
Partial Differential Equations

Existence and stability of periodic solution of contrast structure type in discontinuous singularly perturbed reaction–convection–diffusion problem

Xiao Wua, Mingkang Nib

a School of Mathematical Sciences, East China Normal University, 201100 Shanghai, P. R. China
b Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, 200000 Shanghai, P. R. China
DOI: https://doi.org/10.31857/S0044466922100118
Abstract: A singularly perturbed periodic problem is investigated for the reaction–diffusion–advection equation in the case of a discontinuous source and weak advection. An asymptotic approximation for a periodic solution with an internal transition layer is constructed by using the boundary function method. The asymptotic method of differential inequalities is used to prove the existence of the solution and its asymptotic stability. An example is given and numerical calculations are performed to illustrate the theoretical result.
Key words: singularly perturbed parabolic problems, Internal transition layer, Lyapunov asymptotic stability, discontinuous reactive term.
Funding agency Grant number
National Natural Science Foundation of China 11871217
Science and Technology Commission of Shanghai Municipality 18dz2271000
This paper was supported by the National Natural Science Foundation of China (no. 11871217) and the Science and Technology Commission of Shanghai Municipality (no. 18dz2271000).
Received: 09.11.2021
Revised: 28.12.2021
Accepted: 08.06.2022
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 10, Pages 1664–1679
DOI: https://doi.org/10.1134/S0965542522100116
Bibliographic databases:
Document Type: Article
UDC: 519.624
Language: English
Citation: Xiao Wu, Mingkang Ni, “Existence and stability of periodic solution of contrast structure type in discontinuous singularly perturbed reaction–convection–diffusion problem”, Zh. Vychisl. Mat. Mat. Fiz., 62:10 (2022), 1695; Comput. Math. Math. Phys., 62:10 (2022), 1664–1679
Citation in format AMSBIB
\Bibitem{WuNi22}
\by Xiao~Wu, Mingkang~Ni
\paper Existence and stability of periodic solution of contrast structure type in discontinuous singularly perturbed reaction–convection–diffusion problem
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 10
\pages 1695
\mathnet{http://mi.mathnet.ru/zvmmf11461}
\crossref{https://doi.org/10.31857/S0044466922100118}
\elib{https://elibrary.ru/item.asp?id=49344338}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 10
\pages 1664--1679
\crossref{https://doi.org/10.1134/S0965542522100116}
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