Regularity of weak solution to Maxwell's equations and applications to microwave heating
type: Item
instance of: scholarly article
title: Regularity of weak solution to Maxwell's equations and applications to microwave heating
zbMATH Open document ID: 1068.35169
author: Hong-Ming Yin
published in: Journal of Differential Equations
publication date: 2004-10-01T00:00:00Z
review text: The regularity of a weak solution of the time-harmonic Maxwell equations is considered in a bounded anisotropic medium \(\Omega\), and it is shown that the weak solution of the linearly-degenerate system \(\nabla\times(\gamma(x)\nabla\times{\mathbf E})+ \xi(x){\mathbf E}={\mathbf J}(x)\), \(x\in\Omega\subset\mathbb{R}^3\) is Hölder continuous under regularity conditions for \(\gamma(x)\) and \(\xi(x)\). A coupled electric and temperature microwave heating system is then examined, and it is shown that under certain conditions the system has a weak solution. Then, finally, the existence of a global classical solution is shown to exist for the special case where the electric wave only propagates in one direction.
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35D10
zbMATH DE Number: 2104508
zbMATH Keywords: Time-harmonic Maxwell's equations
zbMATH Keywords: Microwave heating model
zbMATH Keywords: Existence and regularity weak solutions
reviewed by: Alan Jeffrey
MaRDI profile type: Publication
full work available at URL: j.jde.2004.01.010
OpenAlex ID: W2068289874
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DOI: 10.1016/J.JDE.2004.01.010
description: scientific article; zbMATH DE number 2104508