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Vestnik Samarskogo Universiteta. Estestvenno-Nauchnaya Seriya, 2021, Volume 27, Issue 3, Pages 22–30
DOI: https://doi.org/10.18287/2541-7525-2021-27-3-22-30 (Mi vsgu661) 		 
Mathematics

Decomposition of traveling waves problems

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

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/10.18287/2541-7525-2021-27-3-22-30
Abstract: In the article, the traveling waves problem for singularly perturbed systems of semilinear parabolic equations is considered. An effective method for the order reduction of singularly perturbed systems is proposed. The obtained mathematical results are used to study traveling waves both for abstract partial differential equations and for a specific model that can arise in physics problems, chemistry, and biology.
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
This work was supported by a grant from the Russian Foundation for Basic Research and the GFES within the framework of the scientific project No. 20-51-53008 and the NSFC project No. 12011530062.
Received: 02.09.2021
Revised: 09.10.2021
Accepted: 15.11.2021
Document Type: Article
UDC: 517.928
Language: Russian
Citation: V. A. Sobolev, E. A. Tropkina, E. A. Shchepakina, L. Zhang, “Decomposition of traveling waves problems”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 27:3 (2021), 22–30
Citation in format AMSBIB
\Bibitem{SobTroShc21}
\by V.~A.~Sobolev, E.~A.~Tropkina, E.~A.~Shchepakina, L.~Zhang
\paper Decomposition of traveling waves problems
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2021
\vol 27
\issue 3
\pages 22--30
\mathnet{http://mi.mathnet.ru/vsgu661}
\crossref{https://doi.org/10.18287/2541-7525-2021-27-3-22-30}
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    		Вестник Самарского государственного университета. Естественнонаучная серия
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