A nonlinear drift-diffusion model for semiconductors is analyzed to show the existence of non-vacuum global solutions and stationary solutions. The long time behavior of the solutions is studied by establishing the existence of an absorbing set and a compact attractor of the dynamical system. Parallel results on vacuum solutions are also obtained under weaker conditions on model parameters.
& Ito, K.
(1999). Solutions to a Nonlinear Drift-Diffusion Model of Semiconductors. Electronic Journal of Differential Equations, 1999 (15), 1-38.