The Vlasov-Poisson-Boltzmann system near Maxwellians

The dynamics of dilute electrons can be modeled by the Vlasov-Poisson-Boltzmann system. where electrons interact with themselves through collisions and with their self-consistent electric field. It is shown that any smooth, periodic initial perturbation of a given global Maxwellian that preserves the same mass, momentum. and total energy (including, both kinetic and electric energy), leads to a unique global-in-time classical solution. The construction of global solutions is based on an energy method with a new estimate of dissipation from the collision: integral(0)(t) ds is positive definite for.solutiotion f(t. x. v) with small amplitude to the Vlasov-Poisson-Boltzmann system (1.4). (C) 2002 Wiley Periodicals. Inc.