## Viscous Quantum Hydrodynamics and Parameter-Elliptic Systems

2009
Chen, Li
##### Series
Konstanzer Schriften in Mathematik; 263
Preprint
##### Abstract
The viscous quantum hydrodynamic model derived for semiconductor simulation is studied in this paper. The principal part of the vQHD system constitutes a parameter-elliptic operator provided that boundary conditions satisfying the Shapiro-Lopatinskii criterion are specified. We classify admissible boundary conditions and show that this principal part generates an analytic semigroup, from which we then obtain the local in time well-posedness. Furthermore, the exponential stability of zero current and large current steady states is proved, without any kind of subsonic condition. The decay rate is given explicitly.
510 Mathematics
##### Cite This
ISO 690DREHER, Michael, Li CHEN, 2009. Viscous Quantum Hydrodynamics and Parameter-Elliptic Systems
BibTex
@unpublished{Dreher2009Visco-749,
year={2009},
title={Viscous Quantum Hydrodynamics and  Parameter-Elliptic Systems},
author={Dreher, Michael and Chen, Li}
}

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Yes