A nonlinear parabolic system arising from the eddy currents problem
type: Item
instance of: scholarly article
title: A nonlinear parabolic system arising from the eddy currents problem
zbMATH Open document ID: 0962.35083
DOI: 10.1016/S0362-546X(99)00113-3
author: Qi Hong Chen
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2000-10-03T00:00:00Z
review text: The author considers a quasilinear parabolic system of second-order equations with ``quadratic gradient growth nonlinearity''. The problem under consideration is ``the mathematical formulation for the eddy currents problem''. This is when ``small pieces of metal are brought to the melting point with the Joule heating resulting from the eddy currents induced by an external variable magnetic field''. The main body of the paper consists of the existence, uniqueness and regularity results. Estimates of the solutions in different norms as well as some ``potential analysis'' enrich the material of the paper.
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 1513293
zbMATH Keywords: \(L^{1,\gamma}\) estimate
zbMATH Keywords: quadratic gradient growth
zbMATH Keywords: existence, uniqueness and regularity results
reviewed by: Jan W. Cholewa
MaRDI profile type: Publication
cites work: On two problems of electrical heating of conductors
cites work: Q5562267
full work available at URL: s0362-546x(99)00113-3
OpenAlex ID: W2081222479
description: scientific article; zbMATH DE number 1513293