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Model. Anal. Inform. Sist., 2016, Volume 23, Number 3, Pages 283–290 (Mi mais497)  

This article is cited in 1 scientific paper (total in 1 paper)

The asymptotical analysis for the problem of modeling the gas admixture in the surface layer of the atmosphere

M. A. Davydova, N. T. Levashova, S. A. Zakharova

Lomonosov Moscow State University, Faculty of Physics, Leninskiye Gory, 1, bld. 2, Moscow, 119991, Russia

Abstract: In the present work the model boundary value problem for a stationary singularly perturbed reaction-diffusion-advection equation arising at the description of gas impurity transfer processes in an ecosystem "forest – swamp" is considered. Application of a boundary functions method and an asymptotic method of differential inequalities allow to construct an asymptotics of the boundary layer type solution, to prove the existence of the solution with such an asymptotics and its asymptotic stability by Lyapunov as the stationary solution of the corresponding parabolic problem with the definition of local area of boundary layer type solution formation. The latter has a certain importance for applications, since it allows to reveal the solution describing one of the most probable conditions of the ecosystem. In the final part of the work sufficient conditions for existence of solutions with interior transitional layers (contrast structures) are discussed.

Keywords: reaction-diffusion-advection type equations, contrast structures.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00437_а
Russian Science Foundation 14-14-00956
This work was supported by Russian fund of basic researches, project 16-01-00473. The building of the asymptotic approach of the solution and the phase portraits creation were made by S.A. Zakharova with support of Russian Science Foundation 14-14-00956.


DOI: https://doi.org/10.18255/1818-1015-2016-3-283-290

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Bibliographic databases:

UDC: 517.9
Received: 20.05.2016

Citation: M. A. Davydova, N. T. Levashova, S. A. Zakharova, “The asymptotical analysis for the problem of modeling the gas admixture in the surface layer of the atmosphere”, Model. Anal. Inform. Sist., 23:3 (2016), 283–290

Citation in format AMSBIB
\Bibitem{DavLevZak16}
\by M.~A.~Davydova, N.~T.~Levashova, S.~A.~Zakharova
\paper The asymptotical analysis for the problem of modeling the gas admixture in the surface layer of the atmosphere
\jour Model. Anal. Inform. Sist.
\yr 2016
\vol 23
\issue 3
\pages 283--290
\mathnet{http://mi.mathnet.ru/mais497}
\crossref{https://doi.org/10.18255/1818-1015-2016-3-283-290}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3520849}
\elib{http://elibrary.ru/item.asp?id=26246293}


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    This publication is cited in the following articles:
    1. N. T. Levashova, O. A. Nikolaeva, “Asimptoticheskoe issledovanie resheniya uravneniya teploprovodnosti vblizi granitsy razdela dvukh sred”, Model. i analiz inform. sistem, 24:3 (2017), 339–352  mathnet  crossref  elib
  • Моделирование и анализ информационных систем
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