Existence of weak solutions of the drift diffusion model coupled with Maxwell's equations
type: Item
instance of: scholarly article
title: Existence of weak solutions of the drift diffusion model coupled with Maxwell's equations
zbMATH Open document ID: 0887.35147
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-05-25T00:00:00Z
review text: The paper is concerned with the system \[ {\partial\rho_k\over\partial t}= -\text{div }J_k-R,\quad k=1,2,\tag{1} \] \[ {\partial E\over\partial t}= \text{curl }H+ J_2- J_1,\quad {\partial H\over\partial t}= -\text{curl }E,\tag{2} \] \[ \text{div }E= \rho_1- \rho_2+ C,\quad \text{div }H= 0,\tag{3} \] where \(\rho_1\), \(\rho_2\) = densities of holes and electrons, respectively, \(J_1=-D_1\nabla \rho_1+ \mu_1\rho_1 E\), \(J_2= -D_2\nabla\rho_2- \mu\rho_2 E\) are the current densities, \(R\) = recombination/generation of carriers, and \(E\), \(H\) = electromagnetic field. System (1)--(3) is considered in \(\Omega\times (0,+\infty)\) (\(\Omega\subset\mathbb{R}^3\) a bounded Lipschitz domain) and completed by mixed boundary conditions on \(\rho_1\), \(\rho_2\), \(E\), and \(H\) and initial conditions. The author proves the existence of a weak solution to (1)--(3) on any interval \((0,T)\) \((0<T<+\infty)\) by solving a regularized system via the contraction mapping principle, establishing a-priori-estimates on the solutions of the regularized system and then passing to the limit by using compactness arguments.
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 1005592
zbMATH Keywords: drift-diffusion equations
zbMATH Keywords: Maxwell equations
author: Frank Jochmann
reviewed by: Joachim Naumann
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0460
OpenAlex ID: W2094830383
DOI: 10.1006/JMAA.1996.0460
description: scientific article; zbMATH DE number 1005592