Quasi-hydrodynamic semiconductor equations
type: Item
instance of: scholarly article
title: Quasi-hydrodynamic semiconductor equations
zbMATH Open document ID: 0969.35001
published in: Progress in Nonlinear Differential Equations and Their Applications
publication date: 2001-02-22T00:00:00Z
review text: The book under review is devoted to the following three different quasi-hydrodynamic models in semiconductor theory: the isentropic drift-diffusion model, the energy-transport model, and the quantum hydrodynamic model. The author presents the (formal) derivation of each of the models and develops both mathematical analysis and numerical approximation for the three classes of models. Chapter 1 is concerned with the discussion of a hierarchy of kinetic and quasi-hydrodynamic semiconductor equations. The connections between the various {(semi-)} classical and quantum models are explained. Then the three quasi-hydrodynamic models are considered in more detail. The second chapter presents a short summary of the physics and properties of semiconductors. The author explains the basic notions of the structure of homogeneous and inhomogeneous semiconductor devices. The main part of the book are the Chapters 3-5. Chapter 3 is devoted to the study of the isentropic drift-diffusion equations. These equations form a degenerate parabolic-elliptic system. It is derived from a drift-diffusion system incorporating general Fermi-Dirac statistics. The author proves results on the existence of transient solutions, the uniqueness of transient solutions, the localization of vacuum solutions and numerical approximations by mixed finite element discretization in one and two space dimensons. Chapter 4 starts with the derivation of the energy-transport model from the Boltzmann equation by using a Hilbert expansion method. The following discussion is then concerned with a slightly more general energy-transport model. Then a transformation of the variables which symmetrizes the equations, and an entropy function are discussed. Using these tools the author proves results on the existence of transient solutions, long-time behavior of the transient solution, regularity and uniqueness of transient solutions, existence and uniqueness of steady-state solutions and numerical approximation by mixed fi…
reviewed by: Joachim Naumann
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 82D37
Mathematics Subject Classification ID: 81V99
zbMATH DE Number: 1568495
zbMATH Keywords: isentropic drift-diffusion model
zbMATH Keywords: energy-transport model
zbMATH Keywords: hierarchy of kinetic and quasi-hydrodynamic semiconductor equations
zbMATH Keywords: quantum hydrodynamic model
zbMATH Keywords: degenerate parabolic-elliptic system
zbMATH Keywords: transient solutions
zbMATH Keywords: vacuum solutions
author: Ansgar Jüngel
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1568495