Abstract
We prove that the solution of the Vlasov-Fokker-Planck equation converges to the unique stationary solution with same mass as time tends to infinity. The same result holds in the repulsive coulombic case for the Vlasov-Poisson-Fokker-Planck system; the newtonian attractive case is also studied. We establish positive and negative answers to the question of existence of a stationary solution for the last problem by examining the Poisson-Boltzmann equation.
Citation
F. Bouchut. J. Dolbeault. "On long time asymptotics of the Vlasov-Fokker-Planck equation and of the Vlasov-Poisson-Fokker-Planck system with Coulombic and Newtonian potentials." Differential Integral Equations 8 (3) 487 - 514, 1995. https://doi.org/10.57262/die/1369316501
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