The diffraction problem for a half plane with different face impedances revisited
type: Item
instance of: scholarly article
title: The diffraction problem for a half plane with different face impedances revisited
zbMATH Open document ID: 0693.47024
DOI: 10.1016/0022-247X(89)90080-2
author: F. S. Teixeira
author: António F. dos Santos
author: A. B. Lebre
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: In the complement of a ``screen'' \(\{x\in {\mathbb{R}}^ 3|\) \(x_ 2=0\wedge x_ 1\geq 0\}\) the authors consider a special boundary value problem for Maxwell's equation which may be reduced to an interface problem for Helmholtz's equation \((\Delta +k^ 2)\phi =0\) in \({\mathbb{R}}^ 2\) with certain transmission conditions at \(x_ 1=0\). Only the case of a dissipative medium is treated (i.e. Im k\(>0)\) therefore the condition at infinity may be formulated as \(\lim \phi (x_ 1,x_ 2)=0\) as \(| x_ 2| \to \infty\). If the desired solution \(\phi\) is viewed upon as an element \(\phi (\cdot,x_ 2)\in {\mathcal S}'({\mathbb{R}})\) an equivalent Wiener-Hopf formulation may be derived. The authors show that the theory of singular integral operators may be applied successfully to this system of Wiener-Hopf equations once the right Sobolev spaces \(H^{\alpha}\) are chosen for \(\phi (\cdot,x_ 2)\).
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 78A45
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 4134886
zbMATH Keywords: boundary value problem for Maxwell's equation
zbMATH Keywords: interface problem for Helmholtz's equation
zbMATH Keywords: dissipative medium
zbMATH Keywords: Wiener-Hopf formulation
zbMATH Keywords: singular integral operators
zbMATH Keywords: Wiener-Hopf equations
zbMATH Keywords: Sobolev spaces
reviewed by: Norbert Weck
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4134886