The Euler–Poisson equations describe important physical phenomena in many applications such as semiconductor modeling and plasma physics. This paper is to advance our understanding of critical threshold phenomena in such systems in the presence of different forces. We identify critical thresholds in two damped Euler–Poisson systems, with and without alignment, both with attractive potential and spatially variable background state. For both systems, we give respective bounds for subcritical and supercritical regions in the space of initial configuration, thereby proving the existence of a critical threshold for each scenario. Key tools include comparison with auxiliary systems and the phase space analysis of the transformed system.

欧拉-泊松方程描述了许多应用中的重要物理现象，例如半导体建模和等离子体物理。本文旨在增进我们对存在不同作用力时此类系统中临界阈值现象的理解。我们确定了两个阻尼欧拉-泊松系统的临界阈值，有和没有对准，都具有潜在的吸引力和空间可变的背景状态。对于这两个系统，我们在初始配置的空间中分别给出了亚临界和超临界区域的界限，从而证明了每种情况下都存在临界阈值。关键工具包括与辅助系统的比较以及转换后系统的相空间分析。