## 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 if a

certain term can be ignored, the solutions are unique.

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.

Original language | English |
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Publisher | [Publisher information missing] |

Number of pages | 20 |

Volume | TEAT-7095 |

Publication status | Published - 2001 |

### Publication series

Name | Technical Report LUTEDX/(TEAT-7095)/1-20/(2001) |
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Volume | TEAT-7095 |

### Bibliographical note

Published version: Progress In Electromagnetics Research, Vol. 71, pp. 317-339, 2007.## Subject classification (UKÄ)

- Electrical Engineering, Electronic Engineering, Information Engineering