Analysis of a non-uniformly elliptic and nonlinear coupled parabolic–elliptic system arising in steel hardening

The goal of this work is to analyse the existence of weak solutions to a coupled nonlinear parabolic–elliptic system derived from the heating industrial process of a steel workpiece, and whose unknowns are the electric potential, the magnetic vector potential and the temperature. We introduce the ha...

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Bibliographic Details
Authors: González Montesinos, María Teresa, Ortegón Gallego, Francisco
Format: article
Status:Versión enviada para evaluación y publicación
Publication Date:2013
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/89107
Online Access:https://hdl.handle.net/11441/89107
https://doi.org/10.1080/00207160.2013.771837
Access Level:Open access
Keyword:Steel hardening
Maxwell’s equations
Joule’s heating
Nonlinear parabolic–elliptic equations
Sobolev spaces
Description
Summary:The goal of this work is to analyse the existence of weak solutions to a coupled nonlinear parabolic–elliptic system derived from the heating industrial process of a steel workpiece, and whose unknowns are the electric potential, the magnetic vector potential and the temperature. We introduce the harmonic regime because of the different time scales related to the electric potential and the magnetic vector potential versus the temperature. This lead us to a new system of nonlinear partial differential equations.