Pseudodifferential operator method in a problem on the diffraction of an electromagnetic wave on a dielectric body
type: Item
instance of: scholarly article
title: Pseudodifferential operator method in a problem on the diffraction of an electromagnetic wave on a dielectric body
zbMATH Open document ID: 1252.35288
DOI: 10.1134/S0012266112040064
author: D. V. Valovik
author: Yu G. Smirnov
published in: Differential Equations
publication date: 2012-08-13T00:00:00Z
review text: The authors consider the following diffraction problem: a solid body \(\Omega\) with boundary \(\partial\Omega\) of class \(C^\infty\) characterized by a constant permeability \(\mu_0\) and a \(C^\infty\) \(3\times3\) permittivity tensor \(\hat\epsilon\) is placed in free space \({\mathbb R}^3\). One constructs the electromagnetic field \(\mathbf E\), \(\mathbf H\) satisfying the Maxwell equations, the continuity conditions for the tangential field components across the boundary, and the radiation conditions at infinity. The problem of finding this field can be reduced to the solution of a multidimensional singular integral equation. The authors suggest an alternative method based on the theory of pseudodifferential operators (\(\psi\)DO). Such method permits one to obtain a number of results on the solvability of Maxwell equations other than previously known results.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 35S15
Mathematics Subject Classification ID: 35Q61
zbMATH DE Number: 6065281
zbMATH Keywords: pseudodifferential operator
zbMATH Keywords: diffraction
zbMATH Keywords: electromagnetic wave
zbMATH Keywords: dielectric body
zbMATH Keywords: Fredholm operator
MaRDI profile type: Publication
cites work: Investigation of Electromagnetic Diffraction by a Dielectric Body in a Waveguide Using the Method of Volume Singular Integral Equation
cites work: Q4204482
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full work available at URL: s0012266112040064
OpenAlex ID: W1967414925
description: scientific article; zbMATH DE number 6065281