Global existence and regularity of solutions to a system of nonlinear Maxwell equations.
type: Item
instance of: scholarly article
title: Global existence and regularity of solutions to a system of nonlinear Maxwell equations.
zbMATH Open document ID: 1039.35122
DOI: 10.1016/S0022-247X(03)00415-3
author: Habib Ammari
author: Kamel Hamdache
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-11-16T00:00:00Z
review text: A model for the propagation of electromagnetic fields in ferroelectric media is considered. The corresponding material relations linking the magnetic induction \(B\) with the magnetic field \(H\) and the displacement current density \(D\) with the electric field \(E\) are \(B=\mu H\), \(\mu \in \mathbb{R}_{>0}\) and \(D=\varepsilon (E+P(E))\), \(\varepsilon \in \mathbb{R}_{>0}\). The current density induced by the electric field is assumed to be proportional to it. The non-linear polarization term \(P(E)\) is itself given as the solution of a Maxwell type system with a Lipschitz continuous lower order non-linearity and a source term proportional to \(E\). The paper establishes global existence, uniqueness and regularity of solutions.
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 78A25
zbMATH DE Number: 2003887
zbMATH Keywords: Maxwell equations
zbMATH Keywords: ferroelectric media
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: regularity
reviewed by: Rainer Picard
MaRDI profile type: Publication
cites work: Q4002877
cites work: Q3784480
cites work: On the long-time behavior of ferroelectric systems
cites work: Global existence and long time behavior of solutions to a model of ferroelectric materials
cites work: Q5679204
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Q4185201
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description: scientific article; zbMATH DE number 2003887