Time-harmonic solutions of some dissipative problems for Maxwell's equations in a three-dimensional half space
type: Item
instance of: scholarly article
title: Time-harmonic solutions of some dissipative problems for Maxwell's equations in a three-dimensional half space
zbMATH Open document ID: 0649.35083
published in: Pacific Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: Time-harmonic solutions of some dissipative problems for Maxwell's equations in a three-dimensional half space are constructed via the principle of limiting absorption which is rigorously justified. The asymptotic behavior of the solutions so constructed for large spatial distances is then determined. This provides the means of specifying uniqueness classes for them (``radiation conditions''). Uniqueness is proved even when surface waves decaying only like \(| x| ^{- 1/2}\) along the boundary (as opposed to spatial waves decaying like \(| x| ^{-1})\) are present. Since time-harmonic solutions are, strictly speaking, physically meaningless, the sense in which the solutions so constructed are approximations for large time to the actual time-dependent solutions is established (the principle of limiting amplitude). Finally, the connection of the present approach with the time-honored Ansatz approach for a point source (e.g., a radiating dipole) is set forth.
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 4059989
zbMATH Keywords: asymptotics
zbMATH Keywords: time-harmonic
zbMATH Keywords: dissipative problems
zbMATH Keywords: Maxwell's equations
zbMATH Keywords: three-dimensional half space
zbMATH Keywords: principle of limiting absorption
zbMATH Keywords: uniqueness
zbMATH Keywords: radiation conditions
zbMATH Keywords: approximations
zbMATH Keywords: principle of limiting amplitude
author: John R. Schulenberger
MaRDI profile type: Publication
full work available at URL: pjm.1990.142.313
OpenAlex ID: W2092687736
DOI: 10.2140/PJM.1990.142.313
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description: scientific article; zbMATH DE number 4059989