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Wave splitting of Maxwell’s equations with anisotropic heterogeneous constitutive relations. (English) Zbl 1192.35174

This is a very interesting article about the applications of Functional Analysis in the context of wave phenomena. In particular, it is devoted to the wave splitting technique of Maxwell’s Equations in anisotropic media. The paper, as the author mentions, is an extension of the formalism previously used in linear anisotropic acoustics that results in a matrix of operators, and hence infinite dimensional. The author expects that the extension of the wave splitting technique to the anisotropic case provide both, a base for new applications of the method and the possibility to generate fast numerical codes. A clear formulation of the problem is given at section 2.3. The paper is excessively technical in some parts. Probably a format more extended like a review or a report would be better for the exposition of the ideas and mathematical details simultaneously. For example, the paper contains an appendix with a list of symbols used in the paper with more than 200 entries.

MSC:

35Q61 Maxwell equations
78A25 Electromagnetic theory (general)
78A40 Waves and radiation in optics and electromagnetic theory
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
46N20 Applications of functional analysis to differential and integral equations
47N20 Applications of operator theory to differential and integral equations
47G30 Pseudodifferential operators
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