论文标题
非本地kpp方程和平均场游戏的知识扩散模型的行进波
Traveling waves for a nonlocal KPP equation and mean-field game models of knowledge diffusion
论文作者
论文摘要
我们分析了经济学家R.E.提出的平均场地游戏模型Lucas和B. Moll（2014）描述了基于知识增长和扩散的经济体系。该模型还原为PDE系统，在该系统中，汉密尔顿 - 雅各比 - 贝尔曼方程与非本地反应项的正向KPP型方程相连。我们研究了这种平均场地游戏系统的行进波的存在，并获得了关键和超临界波的存在。特别是，我们证明了经济学家提出的一个猜想是对所描述的经济的存在，从长远来看，这是预期的稳定增长。我们还提供了不存在的结果，可以阐明参数在经济模型中的作用。
We analyze a mean-field game model proposed by economists R.E. Lucas and B. Moll (2014) to describe economic systems where production is based on knowledge growth and diffusion. This model reduces to a PDE system where a backward Hamilton-Jacobi-Bellman equation is coupled with a forward KPP-type equation with nonlocal reaction term. We study the existence of traveling waves for this mean-field game system, obtaining the existence of both critical and supercritical waves. In particular we prove a conjecture raised by economists on the existence of a critical balanced growth path for the described economy, supposed to be the expected stable growth in the long run. We also provide nonexistence results which clarify the role of parameters in the economic model.
