Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation
François Bolley, Arnaud Guillin, Florent Malrieu (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilistic interpretation to obtain convergence towards equilibrium in Wasserstein distance with an explicit exponential rate. We also prove a propagation of chaos property for an associated particle system, and give rates on the approximation of the solution by the particle system. Finally, a transportation ...