The Asymptotical Analysis for the Problem of Modeling the Gas Admixture in the Surface Layer of the Atmosphere
https://doi.org/10.18255/1818-1015-2016-3-283-290
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.
About the Authors
M. A. Davydova
Lomonosov Moscow State University
Russian Federation
Russian Federation
PhD, Faculty of Physics, Leninskiye Gory, 1, bld. 2, Moscow, 119991, Russia
N. T. Levashova
Lomonosov Moscow State University
Russian Federation
Russian Federation
PhD, Faculty of Physics, Leninskiye Gory, 1, bld. 2, Moscow, 119991, Russia,
S. A. Zakharova
Lomonosov Moscow State University
Russian Federation
Russian Federation
student, Faculty of Physics, Leninskiye Gory, 1, bld. 2, Moscow, 119991, Russia,
References
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Review
For citations:
Davydova M.A., Levashova N.T., Zakharova S.A. The Asymptotical Analysis for the Problem of Modeling the Gas Admixture in the Surface Layer of the Atmosphere. Modeling and Analysis of Information Systems. 2016;23(3):283-290. (In Russ.) https://doi.org/10.18255/1818-1015-2016-3-283-290
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