The global weak solution and relaxation limits of the initial-boundary value problem to the bipolar hydrodynamic model for semiconductors

The convergence and consistency of approximate solutions derived by the mod ified Godunov scheme for the initial-boundary value problem to a bipolar hy drodynamic model for semiconductors are proved using the compensated compac tness framework. The information of weak solutions to satisfy the boundary conditions is also displayed. The zero relaxation limit of the bipolar hydr odynamic model towards the drift-diffusion model is carried out when the cu rrent relaxation time tends to zero.