中科院数学与系统科学研究院

数学研究所

偏微分方程研讨班

报告人：李海梁 教授(首都师范大学)

题  目：Spectrum and Behaviors of Vlasov-Poisson-Boltzmann equations

时  间：2020.12.09（星期三）, 19:30-20:30

地  点：腾讯会议， ID：490 845 008

摘  要：The Vlasov-Poisson-Boltzmann equations can be used to model the transport of charged particles (one carrier or two carriers) under the influence of electrostatic potential force. It is not well understood yet how the electrostatic potential force and/or the mutual interaction between charged particles of different type shall affect the spectrum structures and the asymptotical behaviors of global solutions. In this talk, we present the recent progress on the analysis on the spectrum structure and optimal pointwise space-time behaviors of three dimentional Vlasov-Poisson-Boltzmann equations, and the nonlinear stability of planar wave pattern for the bipolar Vlasov-Poisson-Boltzmann equations, such as including shock profile, rarefaction wave and contact discontinuity. These works are joint with Tong Yang, Ming-Ying Zhong, Yi Wang, and Teng Wang.