Moscow University Physics Bulletin

, Volume 72, Issue 6, pp 518–526 | Cite as

Using Asymptotic Analysis for Developing a One-Dimensional Substance Transport Model in the Case of Spatial Heterogeneity

Theoretical and Mathematical Physics

Abstract

We study a solution with an internal transition layer of a one-dimensional boundary value problem for the stationary reaction–advection–diffusion differential equation that arises in mathematical modeling of transport phenomena in the surface layer of the atmosphere in the case of non-uniform vegetation on the assumption of space isotropy along one of the horizontal axes and neutral atmospheric stratification. The parameters of the model at which a boundary value problem has a stable stationary solution with an internal transition layer localized near the boundary between different vegetation types are provided. The existence of such a solution and its local Lyapunov stability and uniqueness are proven. The results can be used for developing multidimensional substance transfer models in the case of a spatial heterogeneity.

Keywords

contrast structures internal transition layer method of differential inequalities transport equation 

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© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Department of PhysicsMoscow State UniversityMoscowRussia

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