On a One-Dimensional Hydrodynamic Model for Semiconductors with Field-Dependent Mobility

We consider a one-dimensional, isentropic, hydrodynamical model for unipolar semiconductor, with the mobility depending on electric field. The is related to momentum relaxation time, and field-dependent models are commonly used describe occurrence of saturation velocity, that is, limit value electron mean velocity as field increases. For steady state system, we prove existence smooth solutions in subsonic case, suitable assumption function. Furthermore, uniqueness sufficiently small currents.