Aperiodic electromagnetic waves in exterior domains
type: Item
instance of: scholarly article
title: Aperiodic electromagnetic waves in exterior domains
zbMATH Open document ID: 0675.35076
DOI: 10.1016/0022-247X(88)90145-X
author: Peter Werner
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: The paper considers the vectorial wave equation with the electric and magnetic boundary conditions, respectively, corresponding to the assumption of total reflection, in an exterior domain assuming a time- harmonic forcing term of frequency \(\omega\). Main result is that the solution U behaves for large time t like \[ U(t)=tP_{+0}(U_ t(0)- i\omega^{-1}F)+P_{+0}(U(0)+\omega^{-2}F)+o(1)\quad as\quad t\to \infty, \] where \(P_{+0}\) denotes the projection on the null space of the selfadjoint realization of the Laplacian with the above boundary conditions. The result rests on the low frequency behaviour of the related time-harmonic problem. The result is applied to obtain the corresponding asymptotic properties of the solution of the isotropic homogeneous Maxwell's equations.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 78A45
Mathematics Subject Classification ID: 35P25
zbMATH DE Number: 4105468
zbMATH Keywords: vectorial wave equation
zbMATH Keywords: electric and magnetic boundary conditions
zbMATH Keywords: total reflection
zbMATH Keywords: exterior domain
zbMATH Keywords: time-harmonic forcing term
zbMATH Keywords: selfadjoint realization
zbMATH Keywords: Laplacian
zbMATH Keywords: low frequency behaviour
zbMATH Keywords: asymptotic properties
zbMATH Keywords: isotropic homogeneous Maxwell's equations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4105468