Green's Function and Pointwise Space-time Behaviors of the Vlasov-Poisson-Boltzmann System
Green's Function and Pointwise Space-time Behaviors of the Vlasov-Poisson-Boltzmann System
复制标题
Vlasov-Poisson-Boltzmann 系统的格林函数和点时空行为
DOI：
10.1007/s00205-019-01438-w
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发表时间：
2020
影响因子：
2.5
通讯作者：
Zhong Mingying
中科院分区：
文献类型：
--
作者：
Li Hai-Liang;Yang Tong;Zhong Mingying
研究了三维VPB系统的绿色函数的逐点时空行为和整体解。结果表明，由于泊松方程所支配的静电势的影响，绿色函数只允许宏观非线性扩散波、奇异动力学波和在时间上按指数衰减但在空间上按代数衰减的余项.这些行为与玻尔兹曼方程有本质的区别，即VPB系统不能观察到玻尔兹曼方程的惠更斯型声波传播和余项的时空指数衰减（Liu和Yu in Commun Pure Appl Math 57：1543-1608，2004; Bull Inst Math Acad Sin（NS）1（1）：1-78，2006）。进一步，我们利用绿色函数建立了非线性VPB系统整体解的逐点时空非线性扩散行为。介绍了一些新的策略来处理电场引起的困难。
The pointwise space-time behaviors of the Green’s function and the global solution to the Vlasov-Poisson-Boltzmann (VPB) system in spatial three dimension are studied in this paper. It is shown that, due to the influence of electrostatic potential governed by the Poisson equation, the Green’s function admits only the macroscopic nonlinear diffusive waves, the singular kinetic waves, and the remainder term decaying exponentially in time but algebraically in space. These behaviors have an essential difference from the Boltzmann equation, namely, the Huygen’s type sound wave propagation and the space-time exponential decay of remainder term for Boltzmann equation (Liu and Yu in Commun Pure Appl Math 57:1543–1608, 2004; Bull Inst Math Acad Sin (NS) 1(1): 1–78, 2006) cannot be observed for VPB system. Furthermore, we establish the pointwise space-time nonlinear diffusive behaviors of the global solution to the nonlinear VPB system in terms of the Green’s function. Some new strategies are introduced to deal with the difficulties caused by the electric fields.