论文标题
营养消耗驱动的集体运动
Collective motion driven by nutrient consumption
论文作者
论文摘要
描述细胞集体运动的经典问题是由营养素的消费/消耗驱动的运动。在这里，我们分析了最简单的模型之一，以耦合的部分微分方程/普通微分方程系统，我们扩展了该模型，以便获得描述通常观察到的模式的极限。在此限制中，细胞密度集中为移动的狄拉克质量，而营养素会出现不连续性。我们首先进行分析而无需扩散，从而完整地描述了唯一限制。当包括扩散时，我们证明了几个特定的先验估计值，并将该系统解释为异质单位方程。这使我们能够获得一个限制问题，该问题显示了限制动态的浓度效应。
A classical problem describing the collective motion of cells, is the movement driven by consumption/depletion of a nutrient. Here we analyze one of the simplest such model written as a coupled Partial Differential Equation/Ordinary Differential Equation system which we scale so as to get a limit describing the usually observed pattern. In this limit the cell density is concentrated as a moving Dirac mass and the nutrient undergoes a discontinuity. We first carry out the analysis without diffusion, getting a complete description of the unique limit. When diffusion is included, we prove several specific a priori estimates and interpret the system as a heterogeneous monostable equation. This allow us to obtain a limiting problem which shows the concentration effect of the limiting dynamics.
