Asymptotics of Initial Boundary Value Problems for Hydrodynamic and Drift Diffusion Models for Semiconductors

In this paper, we study the asymptotic behavior of the solutions to the boundary value problems for hydrodynamic and drift diffusion models for semiconductors. Under the insulating boundary condition and equal mass condition on electron and doping profile, we prove that the solutions to these two systems converge to the unique stationary solution time asymptotically.