冷碰撞等离子体相对论模型中的稳定化和爆破
Stabilization and blow-up in the relativistic model of cold collisional plasma
摘要：
我们研究了一维冷等离子体相对论模型中电子-离子碰撞因子对柯西问题解的影响，并表明，根据它们的强度和初始数据，两种情况是可能的：要么解保持光滑并稳定到稳态，要么在有限时间内振荡爆破。与非相对论模型相反，当可以获得分离这两种行为的精确条件时，在更复杂的相对论情况下，可以从下面的时间分析估计光滑解的存在和在此期间保证的振荡次数。此外，我们表明，在相对论的情况下，不考虑碰撞，当振荡对应于任意小的偏差从零平衡位置爆破，电子碰撞的存在下，可以抑制爆破足够小的振荡。在此基础上，构造了一种数值算法，其精度阶数仅由初始数据的光滑性决定。数值实验来说明理论结果。从全尺寸物理实验的角度出发，尽可能合理地选择初始条件。
英文摘要：
We study the influence of the factor of electron-ion collisions on the solution of the Cauchy problem in the one-dimensional relativistic model of cold plasma and show that, depending on their intensity and initial data, two scenarios are possible: either the solution remains smooth and stabilizes to a stationary state, or during a finite time the oscillations blowup. In contrast to the nonrelativistic model, when exact conditions can be obtained separating the two behaviors, in a much more complicated relativistic situation, it turns out to be possible to analytically estimate from below the time during which the existence of a smooth solution and the guaranteed number of oscillations during this time. In addition, we show that in contrast to the relativistic case without taking into account collisions, when oscillations corresponding to arbitrarily small deviations from the zero equilibrium position blow up, the presence of electron collisions can suppress the blow-up of sufficiently small oscillations. Further, based on the analysis of characteristics, a numerical algorithm is constructed, the order of accuracy of which is determined only by the smoothness of the initial data. Numerical experiments are presented to illustrate the theoretical results. The initial conditions are chosen as reasonably as possible from the point of view of full-scale physical experiments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
