ZERO-RELAXATION LIMIT OF NON-ISENTROPIC HYDRODYNAMIC MODELS FOR SEMICONDUCTORS

This paper deals with non-isentropic hydrodynamic models for semiconductors with short momentum and energy relaxation times. With the help of the Maxwell iteration, we construct a new approximation and show that periodic initial-value problems of certain scaled non-isentropic hydrodynamic models have unique smooth solutions in a time interval independent of the two relaxation times. Furthermore, it is proved that as the two relaxation times both tend to zero, the smooth solutions converge to solutions of the corresponding semilinear drift-diffusion models.