论文标题
非局部分散Fisher-KPP方程的空间传播
Spatial Propagation in Nonlocal Dispersal Fisher-KPP Equations
论文作者
论文摘要
在本文中，我们关注有关非局部分散Fisher-KPP方程的传播速度的三个问题。首先，我们研究传播速度的迹象，发现它们是由非局部分散的不对称水平和$ f'（0）$确定的，其中$ f $是反应函数。这表明不对称分散可以在三个方面影响空间动力学：它可以确定溶液的空间传播方向，影响平衡状态的稳定性并影响溶液的单调特性。其次，我们通过构建新的较低解决方案并使用新的“前回扩散”方法提供了改进的扩展速度结果证明。第三，我们建立了扩散速度与指数衰减初始数据之间的关系。我们的结果表明，当分散为对称时，随着指数衰减速率的增加，扩散速度会降低。此外，将扩散速度迹象的结果应用于两个特殊情况，在这些情况下，我们提供了更多不对称扩散影响的细节。
In this paper we focus on three problems about the spreading speeds of nonlocal dispersal Fisher-KPP equations. First, we study the signs of spreading speeds and find that they are determined by the asymmetry level of the nonlocal dispersal and $f'(0)$, where $f$ is the reaction function. This indicates that asymmetric dispersal can influence the spatial dynamics in three aspects: it can determine the spatial propagation directions of solutions, influence the stability of equilibrium states, and affect the monotone property of solutions. Second, we give an improved proof of the spreading speed result by constructing new lower solutions and using the new "forward-backward spreading" method. Third, we establish the relationship between spreading speed and exponentially decaying initial data. Our result demonstrates that when dispersal is symmetric, spreading speed decreases along with the increase of the exponentially decaying rate. In addition, the results on the signs of spreading speeds are applied to two special cases where we present more details of the influence of asymmetric dispersal.
