A. Jüngel, J. Milisic:
"A simplified quantum energy-transport model for semiconductors";
Nonlinear Analysis: Real-World Applications, 12 (2011), S. 1033 - 1046.

Kurzfassung deutsch:
Siehe englisches Abstract.

Kurzfassung englisch:
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.

Quantum energy-transport; quantum semiconductors; existence of solutions

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