The convergence and consistency of approximate solutions derived by the modified Godunov scheme for the initial–boundary value problem to a bipolar hydrodynamic model for semiconductors are proved using the compensated compactness framework. The information of weak solutions to satisfy the boundary conditions is also displayed. The zero relaxation limit of the bipolar hydrodynamic model towards the drift-diffusion model is carried out when the current relaxation time tends to zero.
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Hsiao et al. (2000) studied this question.
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