Spectral analysis of a dissipative problem in electrodynamics: The Sommerfeld problem
This paper contains a survey of the authors' work entitled 'The propagation of electromagnetic waves through, along and over a three dimensional conducting half space' [Methoden Verfahren Math. Phys. (to appear)]. A special case of this problem was originally considered in the now classic paper by A. Sommerfeld in 1909. Since that time there have been a tremendous number of articles in engineering and physics literature on special cases of this important physical model. However, the real composition of the electromagnetic field due to general finite energy sources remained unclear. In particular, there has been considerable controversy regarding the existence and properties of the Zenneck surface wave. The extreme length and technical nature of the complete solution found there as well as the rich history and physical importance of this problem provide the motivation for this survey. Furthermore, the techniques used in the work provide a basis for the rigorous mathematical analysis of a great many dissipative problems in electrodynamics within a unified mathematical framework.
representations of contraction semigroups
scientific article; zbMATH DE number 4008916
scientific article