Boundary value problems for the stationary Vlasov-Boltzmann-Poisson equation
Mihai BostanIrene GambaThierry GoudonAlexis Vasseur
82D1078A3535Q99stationary transport equationsplasma physics modelsBoltzmann-Poisson system
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.
Indiana University Mathematics Journal
2010
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10.1512/iumj.2010.59.4025
10.1512/iumj.2010.59.4025
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Indiana Univ. Math. J. 59 (2010) 1629 - 1660
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