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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 10, Pages 1594–1607 (Mi zvmmf10097)  

This article is cited in 9 scientific papers (total in 9 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

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.

DOI: https://doi.org/10.7868/S0044466914100032

Full text: PDF file (253 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:10, 1536–1549

UDC: 519.633
Received: 18.11.2013
Revised: 03.03.2014

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. T. Levashova, O. A. Nikolaeva, A. D. Pashkin, “Simulation of the temperature distribution at the water-air interface using the theory of contrast structures”, Mosc. Univ. Phys. Bull., 70:5 (2015), 341–345  crossref  mathscinet  isi  elib  scopus
    2. N. T. Levashova, A. A. Melnikova, S. V. Bytsyura, “Primenenie metoda differentsialnykh neravenstv dlya obosnovaniya resheniya sistemy parabolicheskikh uravnenii v vide dvizhuschegosya fronta”, Model. i analiz inform. sistem, 23:3 (2016), 317–325  mathnet  crossref  mathscinet  elib
    3. E. A. Antipov, V. T. Volkov, N. T. Levashova, N. N. Nefedov, “Reshenie vida dvizhuschegosya fronta dvumernoi zadachi reaktsiya-diffuziya”, Model. i analiz inform. sistem, 24:3 (2017), 259–279  mathnet  crossref  elib
    4. D. V. Luk'yanenko, V. T. Volkov, N. N. Nefedov, “Dynamically adapted mesh construction for the efficient numerical solution of a singular perturbed reaction-diffusion-advection equation”, Model. i analiz inform. sistem, 24:3 (2017), 322–338  mathnet  crossref  elib
    5. N. N. Nefedov, O. V. Rudenko, “On front motion in a Burgers-type equation with quadratic and modular nonlinearity and nonlinear amplification”, Dokl. Math., 97:1 (2018), 99–103  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus
    6. D. V. Lukyanenko, M. A. Shishlenin, V. T. Volkov, “Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data”, Commun. Nonlinear Sci. Numer. Simul., 54 (2018), 233–247  crossref  mathscinet  isi  scopus
    7. N. T. Levashova, N. N. Nefedov, A. V. Yagremtsev, “Existence of a solution in the form of a moving front of a reaction-diffusion-advection problem in the case of balanced advection”, Izv. Math., 82:5 (2018), 984–1005  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. E. A. Antipov, N. T. Levashova, N. N. Nefedov, “Asimptoticheskoe priblizhenie resheniya uravneniya reaktsiya-diffuziya-advektsiya s nelineinym advektivnym slagaemym”, Model. i analiz inform. sistem, 25:1 (2018), 18–32  mathnet  crossref  elib
    9. Lukyanenko D.V., Volkov V.T., Nefedov N.N., Yagola A.G., “Application of Asymptotic Analysis For Solving the Inverse Problem of Determining the Coefficient of Linear Amplification in Burgers' Equation”, Mosc. Univ. Phys. Bull., 74:2 (2019), 131–136  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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