Abstract
In this paper, we consider the initial value problem for the bipolar Vlasov-Poisson-Boltzmann (bVPB) system and its related modified Vlasov-Poisson-Boltzmann (mVPB) system. We give the spectrum analysis on the linearized bVPB and mVPB systems around an equilibrium state, and show the optimal convergence rate of solutions to the equilibrium. By this, we show that the electric field decays exponentially, that the distribution function tends to the absolute Maxwellian at the optimal convergence rate (1+t)-3/4 for the bVPB system, and that both the electric field and the distribution function converge to the equilibrium state at the optimal rate (1+t)-3/4 for the mVPB system.
© Indiana University Mathematics Journal| Original language | English |
|---|---|
| Pages (from-to) | 665-725 |
| Journal | Indiana University Mathematics Journal |
| Volume | 65 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2016 |
Funding
The research of the first author was partially supported by the National Natural Science Foundation of China (grant nos. 11171228, 11231006, and 11225102), and by the Key Project of Beijing Municipal Education Commission. The research of the second author was supported by the General Research Fund of City University of Hong Kong (grant no. 103412). Research of the third author was supported by the National Natural Science Foundation of China (grant nos. 11301094), the Beijing Postdoctoral Research Foundation (grant no. 2014ZZ-96), and the Guangxi Natural Science Foundation (grant no. 2014GXNSFBA118020). We thank each of these institutions for their assistance.
Research Keywords
- Bipolar Vlasov-Poisson-Boltzmann system
- modified Vlasov-Poisson-Boltzmann
- spectrum analysis
- optimal time decay rates
- EXTERNAL FORCE
- CONVERGENCE RATE
- SYSTEM
- VACUUM