[Zurück]

A. Jüngel, I. Violet:
"The quasineutral limit in the quantum drift-diffusion equations";
Asymptotic Analysis, 53 (2007), S. 139 - 157.

Siehe englisches Abstract.

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.

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