Contributions to Books:
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,
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.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.