Energy-transport and drift-diffusion limits of nonisentropic Euler–Poisson equations

Quantum Energy-Transport and Drift-Diffusion models

We show that Quantum Energy-Transport and Quantum Drift-Diffusion models can be derived through diffusion limits of a collisional Wigner equation. The collision operator relaxes to an equilibrium defined through the entropy minimization principle. Both models are shown to be entropic and exhibit fluxes which are related with the state variables through spatially non-local relations. Thanks to a...

Solving the Drift Diffusion Equations

The Drift Diffusion equations constitute the simplest and most commonly used model for simulating semiconductor devices. This paper contains a comparitive study of the performance and stability of several algorithms that solve these coupled equations without decoupling them. The considered techniques include Successive Over-Relaxation schemes, Nonlinear Conjugate Gradients, and Damped Inexact N...

A Hierarchy of Hydrodynamic Models for Plasmas. Quasi-Neutral Limits in the Drift-Diffusion Equations

The Energy Transport and the Drift Di usionEquations as Relaxation Limits of theHydrodynamic Model

Two relaxation limits of the hydrodynamic model for semiconductors are investigated. Using the compensated compactness tools we show the convergence of (scaled) entropy solutions of the hydrodynamic model to the solutions of the energy transport and the drift{diiusion equations, according respectively to diierent time scales.

Drift-diffusion Limits of Kinetic Models for Chemotaxis: a Generalization

We study a kinetic model for chemotaxis introduced by Othmer, Dunbar, and Alt [22], which was motivated by earlier results of Alt, presented in [1], [2]. In two papers by Chalub, Markowich, Perthame and Schmeiser, it was rigorously shown that, in three dimensions, this kinetic model leads to the classical KellerSegel model as its drift-diffusion limit when the equation of the chemo-attractant i...