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Title: Weak solutions to a time-dependent heat equation with nonlocal radiation boundary condition and arbitrary $p$-summable right-hand side  (English)
Author: Druet, Pierre-Etienne
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940
Volume: 55
Issue: 2
Year: 2010
Pages: 111-149
Summary lang: English
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Category: math
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Summary: 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.
Keyword: radiative heat transfer
Keyword: nonlinear parabolic equation
Keyword: nonlocal boundary condition
Keyword: right-hand side in $L^1$
MSC: 35D05
MSC: 35D30
MSC: 35K05
MSC: 35K15
MSC: 35K20
MSC: 35K55
MSC: 35K59
idZBL: Zbl 1224.35057
idMR: MR2600939
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Date available: 2010-07-20T13:35:13Z
Last updated: 2013-09-20
Stable URL: http://hdl.handle.net/10338.dmlcz/140391
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