英文标题：
《Mathematical modeling of physical capital using the spatial Solow model》
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作者：
Gilberto Gonz\\\'alez-Parra, Benito Chen-Charpentier, Abraham J. Arenas
  and Miguel Diaz-Rodriguez
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最新提交年份：
2015
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英文摘要：
  This research deals with the mathematical modeling of the physical capital diffusion through the borders of the countries. The physical capital is considered an important variable for the economic growth of a country. Here we use an extension of the economic Solow model to describe how the smuggling affects the economic growth of the countries. In this study we rely on a production function that is non-concave instead of the classical Cobb-Douglas production function. In order to model the physical capital diffusion through the borders of the country, we developed a model based on a parabolic partial differential equation that describes the dynamics of physical capital and boundary conditions of Neumann type. Smuggling is present in many borders between countries and may include fuel, machinery and food. This smuggling through the borders is a problematic issue for the country\'s economies. The smuggling problem usually is related mainly to a non-official exchange rate that is different than the official rate or subsides. Numerical simulations are obtained using an explicit finite difference scheme that shows how the physical capital diffusion through the border of the countries. The study of physical capital is a paramount issue for the economic growth of many countries for the next years. The results show that the dynamics of the physical capital when boundary conditions of Neumann type are different than zero differ from the classical economic behavior observed in the classical spatial Solow model without physical capital flux through the borders of countries. Finally, it can be concluded that avoiding the smuggling through the frontiers is an important factor that affects the economic growth of the countries.
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中文摘要：
这项研究涉及通过国家边界的物质资本扩散的数学模型。物质资本被认为是一个国家经济增长的重要变量。在这里，我们使用经济索洛模型的扩展来描述走私如何影响这些国家的经济增长。在这项研究中，我们依赖于一个非凹的生产函数，而不是经典的柯布-道格拉斯生产函数。为了模拟物质资本通过国家边界的扩散，我们开发了一个基于抛物线偏微分方程的模型，该方程描述了物质资本的动力学和Neumann类型的边界条件。国家之间的许多边境都存在走私活动，可能包括燃料、机械和食品。这种跨境走私对该国经济来说是个问题。走私问题通常主要与非官方汇率有关，该汇率与官方汇率不同或有所下降。数值模拟采用显式有限差分格式，显示了物质资本如何通过国家边界扩散。对物质资本的研究是许多国家未来几年经济增长的首要问题。结果表明，当Neumann型边界条件不同于零时，物质资本的动态与在没有物质资本通过国家边界流动的经典空间Solow模型中观察到的经典经济行为不同。最后，可以得出结论，避免边境走私是影响各国经济增长的一个重要因素。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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一级分类：Mathematics        数学
二级分类：Dynamical Systems        动力系统
分类描述：Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
微分方程和流动的动力学，力学，经典的少体问题，迭代，复杂动力学，延迟微分方程
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