On Long Time Asymptotics of the Vlasov-fokker-planck Equation and of the Vlasov-poisson-fokker-planck System with Coulombic and Newtonian Potentials
نویسندگان
چکیده
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.
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