Abstract Learning is the basic thing for a person’s growth, whenever in school or on the work. Also the economic growth of a country depends its technology and science. The knowledge diffusion in a firm dynamic system is important. Some former models have been given by Fernando E. Alvarez, Francisco J. Buera and Robert E. Lucas, Jr’s paper: “Models of Idea Flows” (Alvarez et al., 2008). Our model based on the earlier work but extend the definition of spread direction based on Fourier’s law, in which case can also explain the asymptotic equilibrium state. Solving the partial differential equation helps us to learn the solution well. A simulation is given using finite difference method to sketch the curve moving, also comparing with the realistic economic curves and they are fit. It can well explain the economic stable in the closed system of a single country and a “huge” change under some special outside “source” power.

中文翻译：

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基于傅立叶定律的知识扩散与经济增长

摘要 学习是一个人成长的基础，无论是在学校还是在工作中。一个国家的经济增长也取决于它的技术和科学。企业动态系统中的知识扩散很重要。Fernando E. Alvarez、Francisco J. Buera 和 Robert E. Lucas, Jr 的论文“思想流模型”（Alvarez 等人，2008 年）提供了一些以前的模型。我们的模型基于早期工作，但扩展了基于傅立叶定律的传播方向的定义，在这种情况下，也可以解释渐近平衡状态。求解偏微分方程有助于我们很好地学习解法。用有限差分法模拟了曲线的运动，并与现实的经济曲线进行了比较，它们是拟合的。