Cahiers du CEREMADE 

Unité
Mixte de Recherche du C.N.R.S. N°7534 

Abstract : he relative entropy method describes the irreversibility of the VlasovPoisson and VlasovBoltzmannPoisson systems in bounded domains with incoming boundary conditions. Uniform in time estimates are deduced from the entropy. In some cases, these estimates are sufficient to prove the convergence of the solution to a unique stationary solution, as time goes to infinity. The method is also used to analyze other types of boundary conditions such as mass and energy preserving diffuse reflection boundary conditions, and to prove the uniqueness of stationary solutions for some special collision terms. 





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