Global solution to the drift-diffusion-Poisson system for semiconductors   with nonlinear recombination-generation rate
  In this paper, we study the Cauchy problem of a time-dependent drift-diffusion-Poisson system for semiconductors. Existence and uniqueness of global weak solutions are proven for the system with a higher-order nonlinear recombination-generation rate R. We also show that the global weak solution will converge to a unique equilibrium as time tends to infinity. 
Hao Wu and Jie Jiang
math.AP