中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：Mingying Zhong (Guangxi University)
题 目：Spectrum Analysis for the Vlasov-Poisson-Boltzmann System
时 间：2023.09.22（星期一）10:00-11:00
地 点：腾讯会议：640-168-508
摘 要：By identifying a norm capturing the effect of the forcing governed by the Poisson equation, we give a detailed spectrum analysis on the linearized Vlasov-Poisson-Boltzmann system around a global Maxwellian. It is shown that the electric field governed by the self-consistent Poisson equation plays a key role in the analysis so that the spectrum structure is genuinely different from the well-known one of the Boltzmann equation. Based on this, we give the optimal time decay rates of solutions to the equilibrium.
----------------
题 目：Green's function and pointwise behavior of the Vlasov-Poisson-Boltzmann System
时 间：2023.09.19（星期二）10:00-11:00
地 点：腾讯会议：313-557-794
摘 要：In this talk, we study the pointwise space-time behaviors of the Green's function and the global solution to the Vlasov-Poisson-Boltzmann (VPB) system in whole space. 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 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 can not 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.
附件：