Spectrum analysis and optimal decay rates of the bipolar Vlasov-Poisson-Boltzmann equations

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)665-725
Journal / PublicationIndiana University Mathematics Journal
Issue number2
Publication statusPublished - 2016


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.

Research Area(s)

  • Bipolar Vlasov-Poisson-Boltzmann system, modified Vlasov-Poisson-Boltzmann, spectrum analysis, optimal time decay rates, EXTERNAL FORCE, CONVERGENCE RATE, SYSTEM, VACUUM