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On uniqueness and continuity for the quasi-linear, bianisotropic Maxwell equations, using an entropy condition

Sjöberg, Daniel LU (2007) In Progress in Electromagnetics Research-Pier 71. p.317-339
Abstract
The quasi-linear Maxwell equations describing electromagnetic wave propagation in nonlinear media permit several weak solutions, which may be discontinuous (shock waves). It is often conjectured that the

solutions are unique if they satisfy an additional entropy

condition. The entropy condition states that the energy contained in the electromagnetic fields is irreversibly dissipated to other energy forms, which are not described by the Maxwell equations. We use the method employed by Kruzkov to scalar conservation laws to analyze the

implications of this additional condition in the electromagnetic case, i.e., systems of equations in three dimensions. It is shown that if a cubic term can be ignored, the solutions... (More)
The quasi-linear Maxwell equations describing electromagnetic wave propagation in nonlinear media permit several weak solutions, which may be discontinuous (shock waves). It is often conjectured that the

solutions are unique if they satisfy an additional entropy

condition. The entropy condition states that the energy contained in the electromagnetic fields is irreversibly dissipated to other energy forms, which are not described by the Maxwell equations. We use the method employed by Kruzkov to scalar conservation laws to analyze the

implications of this additional condition in the electromagnetic case, i.e., systems of equations in three dimensions. It is shown that if a cubic term can be ignored, the solutions are unique and depend continuously on given data. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Progress in Electromagnetics Research-Pier
volume
71
pages
317 - 339
publisher
EMW Publishing
external identifiers
  • wos:000246722700018
  • scopus:34147140546
ISSN
1070-4698
DOI
10.2528/PIER07030804
language
English
LU publication?
yes
id
04b69405-a4a6-4ea7-add9-b523c3cf88c8 (old id 637533)
date added to LUP
2007-12-12 12:36:06
date last changed
2017-01-01 04:25:09
@article{04b69405-a4a6-4ea7-add9-b523c3cf88c8,
  abstract     = {The quasi-linear Maxwell equations describing electromagnetic wave propagation in nonlinear media permit several weak solutions, which may be discontinuous (shock waves). It is often conjectured that the<br/><br>
solutions are unique if they satisfy an additional entropy<br/><br>
condition. The entropy condition states that the energy contained in the electromagnetic fields is irreversibly dissipated to other energy forms, which are not described by the Maxwell equations. We use the method employed by Kruzkov to scalar conservation laws to analyze the<br/><br>
implications of this additional condition in the electromagnetic case, i.e., systems of equations in three dimensions. It is shown that if a cubic term can be ignored, the solutions are unique and depend continuously on given data.},
  author       = {Sjöberg, Daniel},
  issn         = {1070-4698},
  language     = {eng},
  pages        = {317--339},
  publisher    = {EMW Publishing},
  series       = {Progress in Electromagnetics Research-Pier},
  title        = {On uniqueness and continuity for the quasi-linear, bianisotropic Maxwell equations, using an entropy condition},
  url          = {http://dx.doi.org/10.2528/PIER07030804},
  volume       = {71},
  year         = {2007},
}