The combined relaxation and vanishing Debye length limit for the hydrodynamic model for semiconductors is considered in both the unipolar and the bipolar case. The resulting limit problems are non-linear drift driven hyperbolic equations. We make use of non-standard entropy functions and the related entropy productions in order to obtain uniform estimates. In the bipolar case additional time-dependent L-infinity-type estimates, available from the existence theory, are needed in order to control the entropy production terms. Finally, strong convergence of the electric field allows the limit towards the limiting problem.
The combined relaxation and vanishing Debye length limit in the hydrodynamic model for semiconductors
PIERANGELO
2001-01-01
Abstract
The combined relaxation and vanishing Debye length limit for the hydrodynamic model for semiconductors is considered in both the unipolar and the bipolar case. The resulting limit problems are non-linear drift driven hyperbolic equations. We make use of non-standard entropy functions and the related entropy productions in order to obtain uniform estimates. In the bipolar case additional time-dependent L-infinity-type estimates, available from the existence theory, are needed in order to control the entropy production terms. Finally, strong convergence of the electric field allows the limit towards the limiting problem.File in questo prodotto:
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