Weak solutions to a time-dependent heat equation with nonlocal radiation boundary condition and arbitrary $p$-summable right-hand side

Druet, Pierre-Etienne. "Weak solutions to a time-dependent heat equation with nonlocal radiation boundary condition and arbitrary $p$-summable right-hand side." Applications of Mathematics 55.2 (2010): 111-149. <http://eudml.org/doc/37841>.

@article{Druet2010,
abstract = {We consider a model for transient conductive-radiative heat transfer in grey materials. Since the domain contains an enclosed cavity, nonlocal radiation boundary conditions for the conductive heat-flux are taken into account. We generalize known existence and uniqueness results to the practically relevant case of lower integrable heat-sources, and of nonsmooth interfaces. We obtain energy estimates that involve only the $L^p$ norm of the heat sources for exponents $p$ close to one. Such estimates are important for the investigation of models in which the heat equation is coupled to Maxwell’s equations or to the Navier-Stokes equations (dissipative heating), with many applications such as crystal growth.},
author = {Druet, Pierre-Etienne},
journal = {Applications of Mathematics},
keywords = {radiative heat transfer; nonlinear parabolic equation; nonlocal boundary condition; right-hand side in $L^1$; radiative heat transfer; nonlinear parabolic equation; nonlocal boundary condition; right-hand side in },
language = {eng},
number = {2},
pages = {111-149},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weak solutions to a time-dependent heat equation with nonlocal radiation boundary condition and arbitrary $p$-summable right-hand side},
url = {http://eudml.org/doc/37841},
volume = {55},
year = {2010},
}

TY - JOUR
AU - Druet, Pierre-Etienne
TI - Weak solutions to a time-dependent heat equation with nonlocal radiation boundary condition and arbitrary $p$-summable right-hand side
JO - Applications of Mathematics
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 2
SP - 111
EP - 149
AB - We consider a model for transient conductive-radiative heat transfer in grey materials. Since the domain contains an enclosed cavity, nonlocal radiation boundary conditions for the conductive heat-flux are taken into account. We generalize known existence and uniqueness results to the practically relevant case of lower integrable heat-sources, and of nonsmooth interfaces. We obtain energy estimates that involve only the $L^p$ norm of the heat sources for exponents $p$ close to one. Such estimates are important for the investigation of models in which the heat equation is coupled to Maxwell’s equations or to the Navier-Stokes equations (dissipative heating), with many applications such as crystal growth.
LA - eng
KW - radiative heat transfer; nonlinear parabolic equation; nonlocal boundary condition; right-hand side in $L^1$; radiative heat transfer; nonlinear parabolic equation; nonlocal boundary condition; right-hand side in
UR - http://eudml.org/doc/37841
ER -