Existence of weak solutions to the time-dependent MHD equations coupled to the heat equation with nonlocal radiation boundary conditions
type: Item
instance of: scholarly article
title: Existence of weak solutions to the time-dependent MHD equations coupled to the heat equation with nonlocal radiation boundary conditions
zbMATH Open document ID: 1173.80002
author: Pierre-Etienne Druet
published in: Nonlinear Analysis. Real World Applications
publication date: 2009-06-09T00:00:00Z
review text: The coupling of the system of magnetohydrodynamics to the heat equation in context of an application to crystal growth is studied. The heat sources are given by the dissipation of current that occurs in the fixed conductors of the system. Following the Boussinesq model the dissipative heating is neglected in the fluid. For the magnetic field the natural interface conditions are taken into account, while the nonlocal radiation boundary conditions are used for the heat flux. The existence of a weak solution with a defect measure is proven -- concentrated in a singular set.
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 82D10
zbMATH DE Number: 5563210
zbMATH Keywords: magnetohydrodynamics
zbMATH Keywords: radiative heat-transfer
zbMATH Keywords: natural interface conditions
zbMATH Keywords: nonlocal radiation boundary conditions
reviewed by: Iván Abonyi
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2008.09.015
OpenAlex ID: W2084132390
cites work: Numerical simulation of industrial crystal growth
cites work: Modeling and simulation of sublimation growth of SiC bulk single crystals
cites work: Q4265804
cites work: Conductive-radiative heat transfer in grey materials
cites work: TRANSIENT CONDUCTIVE–RADIATIVE HEAT TRANSFER: DISCRETE EXISTENCE AND UNIQUENESS FOR A FINITE VOLUME SCHEME
cites work: Q5518219
cites work: The validity of the Boussinesq approximation for liquids and gases
cites work: Q3123386
cites work: Weak solutions to a stationary heat equation with nonlocal radiation boundary condition and right‐hand side in Lp (p⩾1)
cites work: Variational methods for stationary MHD flow under natural interface conditions
cites work: On the existence of weak solutions to the equations of non-stationary motion of heat-conducting incompressible viscous fluids
cites work: The mathematical analysis of the coupling of a turbulent kinetic energy equation to the navier-stokes equation with an eddy viscosity
cites work: The equations of magnetohydrodynamics: on the interaction between matter and radiation in the evolution of gaseous stars
cites work: Q5890172
cites work: Nonlinear elliptic and parabolic equations involving measure data
cites work: Compact sets in the space \(L^ p(0,T;B)\)
cites work: Q4366310
cites work: Q5562267
DOI: 10.1016/J.NONRWA.2008.09.015
description: scientific article; zbMATH DE number 5563210