Spectrum analysis and optimal decay rates of the bipolar Vlasov-Poisson-Boltzmann equations
Spectrum analysis and optimal decay rates of the bipolar Vlasov-Poisson-Boltzmann equations
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DOI：
10.1512/iumj.2016.65.5730
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发表时间：
2014-11
期刊：
影响因子：
--
通讯作者：
Hai-liang Li;Tong Yang;Mingying Zhong
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文献类型：
--
作者：
Hai-liang Li;Tong Yang;Mingying Zhong
本文考虑双极Vlasov-Poisson-Boltzmann（bVPB）系统及其相应的修正Vlasov-Poisson-Boltzmann（mVPB）系统的初值问题.我们给出了线性化bVPB和mVPB系统在平衡点附近的谱分析，并给出了整体解的最优收敛速度。结果表明，bVPB系统在最佳收敛速度$（1+t）^{-3/4}$下，电场指数衰减，分布函数趋于绝对麦克斯韦分布，而mVPB系统在最佳收敛速度$（1+t）^{-3/4}$下，电场和分布函数均收敛到平衡态.
In the present paper, we consider the initial value problem for the bipolar Vlasov-Poisson-Boltzmann (bVPB) system and its corresponding modified Vlasov-Poisson-Boltzmann (mVPB). We give the spectrum analysis on the linearized bVPB and mVPB systems around their equilibrium state and show the optimal convergence rate of global solutions. It was showed that the electric field decays exponentially and the distribution function tends to the absolute Maxwellian at the optimal convergence rate $(1+t)^{-3/4}$ for the bVPB system, yet both the electric field and the distribution function converge to equilibrium state at the optimal rate $(1+t)^{-3/4}$ for the mVPB system.