Spectral analysis of a dissipative problem in electrodynamics: The Sommerfeld problem
type: Item
instance of: scholarly article
title: Spectral analysis of a dissipative problem in electrodynamics: The Sommerfeld problem
zbMATH Open document ID: 0622.35007
DOI: 10.1007/BF00046935
author: John R. Schulenberger
author: D. S. Gilliam
published in: Acta Applicandae Mathematicae
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35F10
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 35P10
Mathematics Subject Classification ID: 78A40
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4008916
zbMATH Keywords: maximal dissipative operator
zbMATH Keywords: generalized eigenfunction expansion
zbMATH Keywords: representations of contraction semigroups
zbMATH Keywords: electromagnetic wave propagation
zbMATH Keywords: Zenneck surface wave
zbMATH Keywords: survey
zbMATH Keywords: dissipative problems
zbMATH Keywords: electrodynamics
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4008916