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 (Моделирование и анализ информационных систем)
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.