A. Jüngel, I. Violet:

"The quasineutral limit in the quantum drift-diffusion equations";

Asymptotic Analysis,53(2007), 139 - 157.

The quasineutral limit in the transient quantum drift-diffusion

equations in one space dimension is rigorously proved. The model

consists of a fourth-order parabolic equation for the electron density,

including the quantum Bohm potential, coupled to the Poisson equation

for the electrostatic potential. The equations are supplemented with

Dirichlet-Neumann boundary conditions. For the proof

uniform a priori bounds for the solutions of the semi-discretized

equations are derived from so-called entropy functionals.

The drift term involving the electrostatic potential is estimated

by proving a new bound for the electric energy. Since the electrostatic

potential is not an admissible test function, an auxiliary test function

has to be carefully constructed.

Siehe englisches Abstract.

Quantum drift-diffusion model, entropy estimates, quasi-neutral limit

Created from the Publication Database of the Vienna University of Technology.