A singular limit in a nonlinear problem arising in electromagnetism
type: Item
instance of: scholarly article
title: A singular limit in a nonlinear problem arising in electromagnetism
zbMATH Open document ID: 1237.35152
author: Frank Jochmann
published in: Communications on Pure and Applied Analysis
publication date: 2011-12-19T00:00:00Z
review text: Initial boundary value problems associated with Maxwell's equations for linear media with non-linear conducting inclusions are considered. The limit of vanishing dielectricity \(\epsilon\) in the conducting region leading to the eddy current approximation with a non-linear Ohm's law is of particular interest. Based on existence and uniqueness for the positive dielectricity case, existence of the eddy current limit case is shown by controlling the singular limit \(\epsilon\to0^+\) in the non-linearly conducting region. The limit problem is of hyperbolic-parabolic mixed type. In the two final sections of the paper weak and strong asymptotics of the solution to the limit problem for large times are considered.
reviewed by: Rainer Picard
Mathematics Subject Classification ID: 35Q61
Mathematics Subject Classification ID: 35M10
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 78A35
zbMATH DE Number: 5989616
zbMATH Keywords: Maxwell's equations
zbMATH Keywords: non-linear Ohm's law
zbMATH Keywords: hyperbolic-parabolic mixed type
zbMATH Keywords: singular limits
zbMATH Keywords: asymptotic behavior
MaRDI profile type: Publication
full work available at URL: cpaa.2011.10.541
OpenAlex ID: W2333419219
DOI: 10.3934/CPAA.2011.10.541
description: scientific article; zbMATH DE number 5989616