We clea.l with the long time of the Vlassov-Poisson-Boltzmann system. We present some results on the stationary states with fixed mass and temperature, and prove the convergence of the solutions of the evolution problem towards such states. Then, using the conservation laws, we are able to prove the existence and the uniqueness of the asymptotic state, and to identify its parameters in terms of the conserved quantities of the evolution problem.
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