Publications in Scientific Journals:
L. Chen, X. Chen, A. Jüngel:
"Semiclassical limit in a simplified quantum energy-transport model for semiconductors";
Kinetic and Related Models,
4
(2011),
4;
1049
- 1062.
English abstract:
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.
German abstract:
Siehe englisches Abstract.
Keywords:
Semiclassical limit; quantum corrections; fourth-order equations
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.3934/krm.2011.4.1049
Created from the Publication Database of the Vienna University of Technology.