Knowledge Diffusion and economic Growth based on Fourier’s law

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.