article

Title: Boundary value problems for the stationary Vlasov-Boltzmann-Poisson equation

Authors: Mihai Bostan, Irene M. Gamba, Thierry Goudon and Alexis Vasseur

Issue: Volume 59 (2010), Issue 5, 1629-1660

Abstract:

We investigate the well posedness of stationary Vlasov-Boltzmann equations both in the simpler case of a linear problem with a space varying force field and a collisional integral satisfying the detailed balance principle with a non-singular scattering function, and, the non-linear Vlasov-Poisson-Boltzmann system. For the former we obtain existence-uniqueness results for arbitrarily large integrable boundary data and justify further a priori estimates. For the later the boundary data needs to satisfy an entropy condition guaranteeing classical statistical equilibrium at the boundary. This stationary problem relates to the existence of phase transitions associated with slab geometries.