L. Chen, X. Chen, A. Jüngel:

"Semiclassical limit in a simplified quantum Energy-transport model for semiconductors";

in: "ASC Report 09/2011", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9.

The semiclassical limit in a quantum energy-transport model for semiconductors

is proved. The system consists of a nonlinear parabolic fourth-order equation for

the electron density, including temperature gradients; a degenerate elliptic 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 asymptotic

limit is based on a priori estimates independent of the scaled Planck constant,

obtained from entropy functionals, on the use of Gagliardo-Nirenberg inequalities, and

weak compactness methods.

http://www.asc.tuwien.ac.at/preprint/2011/asc09x2011.pdf

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