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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 11, Pages 1850–1872
DOI: https://doi.org/10.31857/S0044466921110132 (Mi zvmmf11318) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Partial Differential Equations

Existence and stability of the solution to a system of two nonlinear diffusion equations in a medium with discontinuous characteristics

N. T. Levashova, B. V. Tischenko

Faculty of Physics, Lomonosov Moscow State University, 119991, Moscow, Russia
Citations (6)
DOI: https://doi.org/10.31857/S0044466921110132
Abstract: Asymptotic analysis is used to study the existence, local uniqueness, and asymptotic Lyapunov stability of the solution to a one-dimensional nonlinear parabolic system of the activator–inhibitor type. A specific feature of the problem is the discontinuities of the first kind of the functions on the right-hand sides of the equations. The jump of the functions occurs at a single point of the interval on which the problem is considered. The solution with a large gradient in the vicinity of the discontinuity is studied. The existence and stability theorems are proved using the asymptotic method of differential inequalities.
Key words: system of nonlinear equations, small parameter, inner layers, upper and lower solutions, asymptotics of solution, asymptotic Lyapunov stability.
Funding agency Grant number
Russian Science Foundation 18-11-00042П
This work was supported by the Russian Science Foundation, project no. 18-11-00042П.
Received: 23.12.2020
Revised: 24.03.2021
Accepted: 07.07.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 11, Pages 1811–1833
DOI: https://doi.org/10.1134/S0965542521110130
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: N. T. Levashova, B. V. Tischenko, “Existence and stability of the solution to a system of two nonlinear diffusion equations in a medium with discontinuous characteristics”, Zh. Vychisl. Mat. Mat. Fiz., 61:11 (2021), 1850–1872; Comput. Math. Math. Phys., 61:11 (2021), 1811–1833
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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