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Izv. RAN. Ser. Mat., 2018, Volume 82, Issue 5, Pages 131–152 (Mi izv8669)  

Existence of a solution in the form of a moving front of a reaction-diffusion-advection problem in the case of balanced advection

N. T. Levashova, N. N. Nefedov, A. V. Yagremtsev

Faculty of Physics, Lomonosov Moscow State University

Abstract: We consider the initial-boundary value problem for an equation of reaction-diffusion-advection type in the case when the condition of balanced advection is satisfied. We give an algorithm for constructing an asymptotic representation of a solution which has the form of a moving front, obtain the equation of motion for the point of localization of the front, and prove the existence of that solution. The proof uses the asymptotic method of differential inequalities.

Keywords: equation of reaction-diffusion-advection type, small parameter, asymptotic methods, internal transition layer, motion of a front, differential inequalities.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00437
The research was supported by the Russian Foundation for Basic Research (grant no. 16-01-00437).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/im8669

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English version:
Izvestiya: Mathematics, 2018, 82:5, 984–1005

Bibliographic databases:

UDC: 517.956.4
PACS: 02.30.Jr
MSC: Primary 35K20; Secondary 35A35, 35B25, 35C20, 65M99
Received: 02.03.2017
Revised: 19.09.2017

Citation: 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. RAN. Ser. Mat., 82:5 (2018), 131–152; Izv. Math., 82:5 (2018), 984–1005

Citation in format AMSBIB
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  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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