E. Carlen, R. Esposito, J.L. Lebowitz, R. Marra and A. Rokhlenko
Nonunique Stationary States in Driven Systems; The Weakly Ionized Plasma
(21K, TeX)

ABSTRACT.  We study the electron velocity distribution $f(v, t)$ 
in a weakly ionized spatially homogeneous plasma in an external
electric field $E$.  $f$ satisfies a  Boltzmann type equation in which
there are linear terms representing collisions with ions and neutral particles having a specified
Maxwellian distribution as well as a nonlinear electron-electron (e-e) 
collision term.  Using simplified collision terms we prove that, when e-e collisions dominate, the long time
asymptotic behavior of  $f$ is non-unique 
for certain ranges of $E$.  This provides a rigorous proof of a dynamical
phase transition for a realistic (model) system.