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Stationary transonic solutions of a one-dimensional hydrodynamic model for semiconductors. (English) Zbl 0748.35049
Summary: 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.

##### MSC:
 35Q60 PDEs in connection with optics and electromagnetic theory 76D10 Boundary-layer theory, separation and reattachment, higher-order effects