L. Chen, X. Chen, A. Jüngel:
"Semiclassical limit in a simplified quantum energy-transport model for semiconductors";
Kinetic and Related Models, 4 (2011), 4; S. 1049 - 1062.

Kurzfassung deutsch:
Siehe englisches Abstract.

Kurzfassung englisch:
The semiclassical limit in a quantum energy-transport model for
semiconductors is proved. The system consists of a nonlinear parabolic fourthorder
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.

Semiclassical limit; quantum corrections; fourth-order equations

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