[Zurück]

A. Jüngel, S. Krause, P. Pietra:
"A hierarchy of diffusive higher-order moment equations for semiconductors";
SIAM Journal on Applied Mathematics, 68 (2007), 1; S. 171 - 198.

Siehe englisches Abstract.

A hierarchy of diffusive partial differential equations is derived by a moment
method and a Chapman-Enskog expansion from the semiconductor Boltzmann equation
assuming dominant collisions.
The moment equations are closed by employing the entropy maximization principle
of Levermore. The new hierarchy contains the well-known drift-diffusion model,
the energy-transport equations, and the six-moments model of Grasser et al.
It is shown that the diffusive models are
of parabolic type. Two different formulations of the models are derived:
a drift-diffusion formulation, allowing for a numerical decoupling, and
a symmetric formulation in generalized dual entropy variables, inspired by
nonequilibrium thermodynamics. An entropy inequality (or H-theorem) follows
from the latter formulation.

Semiconductor Boltzmann equation, moment method, Chapman-Enskog expansion, entropy maximization, energy-transport model, higher-order moments