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

Sjöberg, Daniel LU (2001) In Technical Report LUTEDX/(TEAT-7095)/1-20/(2001) TEAT-7095.
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 Kruˇzkov 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... (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 Kruˇzkov 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

certain term can be ignored, the solutions are unique. (Less)
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Technical Report LUTEDX/(TEAT-7095)/1-20/(2001)
volume
TEAT-7095
pages
20 pages
publisher
[Publisher information missing]
language
English
LU publication?
yes
id
a81f1841-bcf3-4298-9c18-580ad9b33575 (old id 525970)
date added to LUP
2007-09-12 11:57:59
date last changed
2016-09-30 15:28:55
@techreport{a81f1841-bcf3-4298-9c18-580ad9b33575,
  abstract     = {The quasi-linear Maxwell equations describing electromagnetic wave propagation<br/><br>
in nonlinear media permit several weak solutions, which may be discontinuous<br/><br>
(shock waves). It is often conjectured that the solutions are unique<br/><br>
if they satisfy an additional entropy condition. The entropy condition states<br/><br>
that the energy contained in the electromagnetic fields is irreversibly dissipated<br/><br>
to other energy forms, which are not described by the Maxwell equations.<br/><br>
We use the method employed by Kruˇzkov to scalar conservation laws<br/><br>
to analyze the implications of this additional condition in the electromagnetic<br/><br>
case, i.e., systems of equations in three dimensions. It is shown that if a<br/><br>
certain term can be ignored, the solutions are unique.},
  author       = {Sjöberg, Daniel},
  institution  = {[Publisher information missing]},
  language     = {eng},
  pages        = {20},
  series       = {Technical Report LUTEDX/(TEAT-7095)/1-20/(2001)},
  title        = {On uniqueness and continuity for the quasi-linear, bianisotropic Maxwell equations, using an entropy condition},
  volume       = {TEAT-7095},
  year         = {2001},
}