题目：Stability Analysis for Some Non-Linear Fokker-Planck Type Equations
摘要：In this talk, I will present the global existence and decay rates of the solutions near Maxwellian for non-linear Fokker--Planck equations and non-linear Vlasov–Poisson–Fokker–Planck equations. The global existence is proved by combining uniform-in-time energy estimates and local solution constructed by Picard type iteration sequence. The decay rates of the nonlinear model is obtained by using the precise spectral analysis of the linear Fokker--Planck operator as well as the energy method. The nonlinearity in the model brings new difficulty for the energy estimates, which is resolved by additional tailored weighted-in-$v$ energy estimates suitable for Fokker--Planck operators.
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