Stability of the Equilibrium to the Vlasov-Poisson-Boltzmann System with Non-constant Background Charge
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We study the global existence of classical solution to the Vlasov-Poisson-Boltzmann system with non-constant background charge. In this case the local Maxwellian is the unique stationary state. We show that this equilibrium is nonlinear stable provided that the initial perturbation is sufficient small. Our result solves an open problem stated by Duan and Yang (SIAM J. Math. Anal. 41(6):2353–2387, 2009) in one dimensional case.
KeywordsVlasov-Poisson-Boltzmann system Non-constant background charge Stability
Mathematics Subject Classification76P05 82C40 35B35
The authors are very grateful to the referees for their helpful suggestions, which improved the earlier version of this paper. Yang is supported by the Fundamental Research Funds for the Central Universities (Grant No. NS2012122). Li is supported by the Fundamental Research Funds for the Central Universities (Grant No. 56XZA14010).