Mathematical models for dispersive electromagnetic waves: an overview
It provides a self-contained overview for researchers studying dispersive electromagnetic waves, but is primarily a review with no new results or quantitative benchmarks.
This paper reviews mathematical models for electromagnetic wave propagation in dispersive isotropic media, focusing on the link between physical requirements (non-dissipativity, passivity) and mathematical properties, using energy techniques, spectral theory, and dispersion analysis.
In this work, we investigate mathematical models for electromagnetic wave propagation in dispersive isotropic media. We emphasize the link between physical requirements and mathematical properties of the models. A particular attention is devoted to the notion of non-dissipativity and passivity. We consider successively the case of so-called local media and general passive media. The models are studied through energy techniques, spectral theory and dispersion analysis of plane waves. For making the article self-contained, we provide in appendix some useful mathematical background.