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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 10, Pages 1594–1607
DOI: https://doi.org/10.7868/S0044466914100032 (Mi zvmmf10097) 		 
This article is cited in 27 scientific papers (total in 27 papers)

Asymptotics of the front motion in the reaction-diffusion-advection problem

E. A. Antipov, N. T. Levashova, N. N. Nefedov

Lomonosov Moscow State University, Faculty of Physics
Full-text PDF (253 kB) Citations (27)
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DOI: https://doi.org/10.7868/S0044466914100032
Abstract: A singularly perturbed initial boundary value problem is considered for a parabolic equation that is known in application as the reaction-diffusion-advection equation. An asymptotic expansion of solutions with a moving front is constructed. This asymptotics is proved by the method of differential inequalities, which is based on well-known comparison theorems and develops the ideas of formal asymptotics for constructing upper and lower solutions in singularly perturbed problems with internal and boundary layers.
Key words: singularly perturbed parabolic problems, reaction-diffusion-advection equations, internal layers, fronts, asymptotic methods, method of differential inequalities.
Received: 18.11.2013
Revised: 03.03.2014
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 10, Pages 1536–1549
DOI: https://doi.org/10.1134/S0965542514100029
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: E. A. Antipov, N. T. Levashova, N. N. Nefedov, “Asymptotics of the front motion in the reaction-diffusion-advection problem”, Zh. Vychisl. Mat. Mat. Fiz., 54:10 (2014), 1594–1607; Comput. Math. Math. Phys., 54:10 (2014), 1536–1549
Citation in format AMSBIB
\Bibitem{AntLevNef14}
\by E.~A.~Antipov, N.~T.~Levashova, N.~N.~Nefedov
\paper Asymptotics of the front motion in the reaction-diffusion-advection problem
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2014
\vol 54
\issue 10
\pages 1594--1607
\mathnet{http://mi.mathnet.ru/zvmmf10097}
\crossref{https://doi.org/10.7868/S0044466914100032}
\elib{https://elibrary.ru/item.asp?id=21957015}
\transl
\jour Comput. Math. Math. Phys.
\yr 2014
\vol 54
\issue 10
\pages 1536--1549
\crossref{https://doi.org/10.1134/S0965542514100029}
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    • This publication is cited in the following 27 articles:
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