Viscous Quantum Hydrodynamics and Parameter-Elliptic Systems
L. Chen and M. Dreher
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.
Math. Meth. Appl. Sci.
34
(2011), 520-531.
A preliminary version of the paper is available
here.
