The combined relaxation and vanishing Debye length limit in the hydrodynamic model for semiconductors

The combined relaxation and vanishing Debye length limit for the hydrodynam ic model for semiconductors is considered in both the unipolar and the bipo lar case. The resulting limit problems are non-linear drift driven hyperbol ic equations. We make use of non-standard entropy functions and the related entropy productions in order to obtain uniform estimates. In the bipolar c ase additional time-dependent L-infinity-type estimates, available from the existence theory, are needed in order to control the entropy production te rms. Finally, strong convergence of the electric field allows the limit tow ards the limiting problem. Copyright (C) 2001 John Wiley & Sons, Ltd.