On uniqueness and continuity for the quasi-linear, bianisotropic Maxwell equations, using an entropy condition
Author
Summary, in English
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.
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.
Publishing year
2007
Language
English
Pages
317-339
Publication/Series
Progress in Electromagnetics Research-Pier
Volume
71
Document type
Journal article
Publisher
EMW Publishing
Topic
- Electrical Engineering, Electronic Engineering, Information Engineering
Status
Published
Research group
- Electromagnetic theory
ISBN/ISSN/Other
- ISSN: 1070-4698