Publications in Scientific Journals:
A. Jüngel, J. Milisic:
"A simplified quantum energy-transport model for semiconductors";
Nonlinear Analysis: Real-World Applications,
12
(2011),
1033
- 1046.
English abstract:
The existence of global-in-time weak solutions to a quantum energy-transport model
for semiconductors is proved. The equations are formally derived from the quantum
hydrodynamic model in the large-time and small-velocity regime. They consist of a
nonlinear parabolic fourth-order equation for the electron density, including temperature
gradients; an elliptic nonlinear heat equation for the electron temperature; and the
Poisson equation for the electric potential. The equations are solved in a bounded domain
with periodic boundary conditions. The existence proof is based on an entropy-type
estimate, exponential variable transformations, and a fixed-point argument. Furthermore,
we discretize the equations by central finite differences and present some numerical
simulations of a one-dimensional ballistic diode.
German abstract:
Siehe englisches Abstract.
Keywords:
Quantum energy-transport; quantum semiconductors; existence of solutions
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1016/j.nonrwa.2010.08.026
Created from the Publication Database of the Vienna University of Technology.