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Teoreticheskaya i Matematicheskaya Fizika, 2023, Volume 215, Number 2, Pages 269–288
DOI: https://doi.org/10.4213/tmf10409 (Mi tmf10409) 		 
Stability of a stationary solution of a system of activator–inhibitor-type equations with a double-scale internal transition layer

N. T. Levashova, D. S. Samsonov

Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia
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DOI: https://doi.org/10.4213/tmf10409
Abstract: We study boundary value problems for systems of second-order ordinary differential equations with quasimonotonicity conditions typical of problems of activator–inhibitor type and with solutions containing domains with large gradients. We obtain sufficient conditions for the existence of a stable stationary solution. Using the asymptotic method of differential inequalities, we prove the existence and stability theorems.
Keywords: internal transition layer, method of differential inequalities, upper and lower solutions, asymptotic approximation, quasimonotonicity conditions.
Received: 20.11.2022
Revised: 09.01.2023
English version:
Theoretical and Mathematical Physics, 2023, Volume 215, Issue 2, Pages 691–708
DOI: https://doi.org/10.1134/S0040577923050082
Bibliographic databases:
Document Type: Article
PACS: 02.30.Hq
MSC: 34B16
Language: Russian
Citation: N. T. Levashova, D. S. Samsonov, “Stability of a stationary solution of a system of activator–inhibitor-type equations with a double-scale internal transition layer”, TMF, 215:2 (2023), 269–288; Theoret. and Math. Phys., 215:2 (2023), 691–708
Citation in format AMSBIB
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\by N.~T.~Levashova, D.~S.~Samsonov
\paper Stability of a~stationary solution of a~system of activator--inhibitor-type equations with a~double-scale internal transition layer
\jour TMF
\yr 2023
\vol 215
\issue 2
\pages 269--288
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\crossref{https://doi.org/10.4213/tmf10409}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4602485}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2023TMP...215..691L}
\transl
\jour Theoret. and Math. Phys.
\yr 2023
\vol 215
\issue 2
\pages 691--708
\crossref{https://doi.org/10.1134/S0040577923050082}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85159496637}
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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