On the basic equations for carrier transport in semiconductors
type: Item
instance of: scholarly article
title: On the basic equations for carrier transport in semiconductors
zbMATH Open document ID: 0642.35038
DOI: 10.1016/0022-247X(86)90330-6
author: Herbert Gajewski
author: Konrad Gröger
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: The authors study the system \[ \partial u_ i/\partial t = D_ i \text{div(grad} u_ i+q_ iu_ i \text{grad} v)-R(u_ 1,u_ 2),\quad i=1,2\text{ in } {\mathbb{R}}_+\times G, \] \[ -\text{div}(a \text{grad} v) = f+u_ 1-u_ 2\text{ in } {\mathbb{R}}_+\times G,\quad u_ 1=U_ i,\quad v=V,\quad i=1,2,\text{ on } {\mathbb{R}}_+\times \Gamma_ D, \] \[ \nu (\text{grad} u_ i+q_ iu_ i \text{grad} v)=0,\quad i=1,2,\text{ on } {\mathbb{R}}_+\times \Gamma_ N, \] \[ a(\partial v/\partial \nu)+bv=g\quad on\quad {\mathbb{R}}_+\times \Gamma_ N,\quad u_ i(0,x)=u_ i^{(0)}(x)\text{ in } G, \] where G is an open subset of \({\mathbb{R}}^ N\) (N\(\leq 3)\), whose boundary is constituted of two disjoint parts \(\Gamma_ D\) and \(\Gamma_ N\), \(D_ 1\), \(D_ 2\), \(g_ 1\) and a are strictly positive constants, \(q_ 2=-q_ 1\) and \({\mathbb{R}}: {\mathbb{R}}^ 2\to {\mathbb{R}}\) is a given nonlinearity. Results on existence, uniqueness and asymptotic behavior of the solution \((u_ 1,u_ 2,v)\) as \(t\to +\infty\) were already proved by the first author [Z. Angew. Math. Mech. 65, 101-108 (1985; Zbl 0579.35016)]. The purpose of the paper is to improve those results. In particular, some regularity assumptions are weakened. The open set G, for instance, is supposed to be only a bounded Lipschitzian domain.
reviewed by: Marco Degiovanni
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 78A35
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 4046250
zbMATH Keywords: carrier transport
zbMATH Keywords: semiconductors
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: regularity assumptions
MaRDI profile type: Publication
cites work: An application of the invariance principle to reaction diffusion equations
cites work: On Existence, Uniqueness and Asymptotic Behavior of Solutions of the Basic Equations for Carrier Transport in Semiconductors
cites work: Q5187610
cites work: Q3749429
cites work: Q4777920
cites work: Q4040640
cites work: Q4134319
cites work: Q5890172
cites work: An Initial Value Problem from Semiconductor Device Theory
cites work: Asymptotic behavior of solutions of transport equations for semiconductor devices
cites work: A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
cites work: Q3260749
cites work: Theory of the Flow of Electrons and Holes in Germanium and Other Semiconductors
cites work: Steady state solutions of diffusion-reaction systems with electrostatic convection
full work available at URL: 0022-247x(86)90330-6
OpenAlex ID: W2059073834
Recommended article: On the long-time behaviour of solutions of the p-Laplacian parabolic system
Recommended article: Q5446920
Recommended article: Q3221007
Recommended article: On solutions of quasilinear wave equations with nonlinear damping terms
Recommended article: The stability of solutions in an initial-boundary reaction-diffusion system
Recommended article: Q4210891
Recommended article: Partly dissipative reaction-diffusion systems and a model of phosphorus diffusion in silicon
Recommended article: Q4824320
Recommended article: Q4883721
Recommended article: Global existence and blow up of solutions for some hyperbolic systems with damping and source terms
description: scientific article; zbMATH DE number 4046250