The periodic problem that arises in the mathematical modeling of the vertical transfer of an anthropogenic impurity in the lower troposphere is considered for the nonlinear diffusion transfer equation. The model problem in dimensionless variables is classified as a nonlinear singularly perturbed reaction—diffusion—advection problem, which is studied by the methods of asymptotic analysis. Using the method of boundary functions and the asymptotic method of differential inequalities based on the principle of comparison, an asymptotic problem solution of arbitrary-order accuracy is constructed with the further substantiation of constructions and the study of this solution for the Lyapunov asymptotic stability property. The results of this work are illustrated using an example that describes the concentration field of a linear substance sink.

中文翻译：

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对流层中人为杂质的垂直迁移建模中具有边界层的周期解

对于非线性扩散转移方程，考虑了对流层低层中人为杂质垂直转移数学模型中出现的周期性问题。无量纲变量中的模型问题被归类为非线性奇摄动反应－扩散－对流问题，通过渐近分析的方法对其进行了研究。利用边界函数方法和基于比较原理的微分不等式渐近方法，通过进一步证明构造，并构造Lyapunov渐近稳定性，研究了任意阶精度的渐近问题解，并对其进行了研究。通过描述线性物质池浓度场的示例说明了这项工作的结果。