Vacuum solution and quasineutral limit of semiconductor drift-diffusion equation

The first half of this paper is concerning with the nonlinear drift-diffusion semiconductor model in d (d?3) dimensional space. The global estimate is achieved on the evolution of support of solution and the finite speed of propagation. The proof is based on the estimate of the weighted norm with special designed weight functions. In the second half, we prove the quasineutral limit locally for 1-dimensional standard drift-diffusion model with discontinuous, sign-changing doping profile.