GLOBAL WEAK SOLUTIONS OF THE ONE-DIMENSIONAL HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

The existence of a global weak solution of the one-dimensional hydrodynamic model for semiconductors is proved by the method of artificial viscosity and the theory of compensated compactness. The system is first regularized and global viscosity-solutions are constructed. Letting the viscosity-parameter tend to zero, we obtain a sequence of viscosity-solutions converging in L(infinity)-weak* to a weak solution of the one-dimensional p-system from isoentropic gas dynamics with an electric field term and momentum relaxation. Since the equations are nonlinear and the convergence is only weak, the theory of Young-measures and compensated compactness is applied to obtain a weak solution of the limit problem.