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Mathematical modeling in task of optimal managing by savings in the middle class

机译：中产阶级节省优化管理任务的数学建模

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Consumption and saving balance issues in the middle class, as the most economically active cluster of society, are the subject of extensive expert discussion and require systematic government regulation. The present paper deals with mathematical model of middle class differentiation by savings which dynamics is described by initial boundary value problem with a parabolic equation. This study aims to investigate a case of savings regulation by changing of non-savers share. The paper presents formulation this problem as an optimal boundary control problem for distributed system of savings. Based on the Lagrange principle, the necessary conditions for the solvability of the problem are derived in the form of an optimization system. The optimal control law establishing the relationship between the non-savers share and the structure of the middle class in terms of savings is obtained. The paper also considers an approach to the numerical implementation of the optimal control model in the Comsol Multiphysics simulation software. An example of model calculating for a region of Russia based on real data is given.
机译：中产阶级的消费和储蓄问题，作为最经济活动的社会集群，是广泛专家讨论的主题，并要求系统的政府监管。本文通过节省了通过抛物线方程的初始边值问题描述了中产阶级差异的数学模型。本研究旨在通过改变非储户分享来调查节约规则的案例。本文介绍了将该问题作为分布式储蓄系统的最佳边界控制问题。基于拉格朗日原理，问题的必要条件以优化系统的形式导出。获得了在节省条件方面建立了非储蓄者份额与中产阶级结构之间关系的最佳控制法。本文还考虑了COMSOL Multiphysics仿真软件中最优控制模型的数值实现的方法。给出了基于实际数据的俄罗斯区域计算的模型示例。

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