Stationary Transonic Solutions of a One–Dimensional Hydrodynamic Model for Semiconductors

We study a hydrodynamic model for semiconductors where the energy equation is replaced by a pressure-density relationship. We construct artificial viscosity solutions, prove BV estimates independent of the viscosity coefficient and study the transonic weak limit. We also study the behavior of the limiting solution at the boundary for subsonic data. We find that a boundary layer can be formed on each side of the boundary and has a condition that determines the possible range of discontinuities for the density.