Using Asymptotic Analysis for Developing a One-Dimensional Substance Transport Model in the Case of Spatial Heterogeneity
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.
Keywordscontrast structures internal transition layer method of differential inequalities transport equation
Unable to display preview. Download preview PDF.
- 2.N. T. Levashova, Yu. V. Mukhartova, and A. V. Ol’chev, Komp’yut. Issled. Model. 8, 355 (2016).Google Scholar
- 3.A. S. Dubov, L. P. Bykova, and S. V. Marunich, Turbulence in Plant Cover (Gidrometeoizdat, Leningrad, 1978).Google Scholar
- 4.S. S. Zilitinkevich, Dynamics of the Atmospheric Boundary Layer (Gidrometeoizdat, Leningrad, 1970).Google Scholar
- 8.Ya. B. Zel’dovich, G. I. Barenblatt, V. B. Librovich, and G. M. Makhviladze, Mathematical Theory of Combustion and Explosion (Nauka, Moscow, 1980).Google Scholar