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Vestnik Samarskogo Universiteta. Estestvenno-Nauchnaya Seriya, 2021, Volume 27, Issue 2, Pages 16–24
DOI: https://doi.org/10.18287/2541-7525-2021-27-2-16-24 (Mi vsgu652) 		 
Mathematics

Critical travelling waves in one model of the "reaction-diffusion" type

V. A. Soboleva, E. A. Tropkinaa, E. A. Shchepakinaa, L. Zhangb, J. Wangb

a Samara National Research University, Samara, Russian Federation
b Shandong University of Science and Technology, Qingdao, Shandong, China
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DOI: https://doi.org/10.18287/2541-7525-2021-27-2-16-24
Abstract: The paper is devoted to the order reduction for critical traveling wave problems for a reaction-diffusion type systems. The mathematical apparatus is based on the geometric theory of singular perturbations and the canards technique. The use of the method of invariant manifolds of singularly perturbed systems allows us to replace the study of traveling waves of the original PDE system by analyzing their profiles in a ODE system of a lower order.
Keywords: singular perturbations, slow invariant manifolds, critical travelling waves, singular perturbations, integral manifold, order reduction, asymptotic expansion, differential equations, fast variables, slow variables.
Funding agency Grant number
Russian Foundation for Basic Research 20-51-53008
National Natural Science Foundation of China 12011530062
The work is supported by a grant from the Russian Foundation for Basic Research and the National Natural Science Foundation of China within the framework of the scientific project No. 20-51-53008 and the NSFC project No. 12011530062.
Received: 18.03.2020
Revised: 20.04.2021
Accepted: 28.05.2021
Document Type: Article
UDC: 517.928
Language: Russian
Citation: V. A. Sobolev, E. A. Tropkina, E. A. Shchepakina, L. Zhang, J. Wang, “Critical travelling waves in one model of the "reaction-diffusion" type”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 27:2 (2021), 16–24
Citation in format AMSBIB
\Bibitem{SobTroShc21}
\by V.~A.~Sobolev, E.~A.~Tropkina, E.~A.~Shchepakina, L.~Zhang, J.~Wang
\paper Critical travelling waves in one model of the ''reaction-diffusion'' type
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2021
\vol 27
\issue 2
\pages 16--24
\mathnet{http://mi.mathnet.ru/vsgu652}
\crossref{https://doi.org/10.18287/2541-7525-2021-27-2-16-24}
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    		Вестник Самарского государственного университета. Естественнонаучная серия
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