Existence and unicity for stationary electromagnetic fields with dissipative boundary conditions
type: Item
instance of: scholarly article
title: Existence and unicity for stationary electromagnetic fields with dissipative boundary conditions
zbMATH Open document ID: 0543.35092
DOI: 10.1007/BF01781062
author: Mauro Fabrizio
author: Barbara Lazzari
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1983-01-01T00:00:00Z
review text: The authors prove existence, uniqueness, and continuous dependence upon the data (the function J) of the a.e. (or weak) solution of the time- harmonic Maxwell equations \(rot E+i\omega \mu H=0,\quad rot H-i\omega \epsilon E=J,\quad x\in \Omega \subset R^ 3,\) with the impedance, or dissipative, boundary condition ''à la Leontovich-Schelkunov-Graffi'' \(E_{\tan g}=\lambda H\wedge n,\) \(x\in \partial \Omega\), where n is the outer normal to \(\partial \Omega\), \(E_{\tan g}\) is the tangential component of E on \(\partial \Omega\), and the impedance \(\lambda\) has positive real part. The case where \(\lambda ={1\over2}(1+i)[2\mu_ 2\omega /\sigma_ 2]^{{1\over2}}\) (with \(\mu_ 2\) and \(\sigma_ 2\) the magnetic permeability and electrical conductivity of the material boundary, respectively) is treated in detail. Well-posedness of the problem fails for \(\lambda =0\) perfectly conducting surface, \(\sigma_ 2=\infty)\).
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35F05
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 3863751
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: continuous dependence
zbMATH Keywords: time-harmonic Maxwell equations
zbMATH Keywords: dissipative, boundary condition
zbMATH Keywords: Well-posedness
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3863751