Weak solutions to a time-dependent heat equation with nonlocal radiation boundary condition and arbitrary <Emphasis Type="Italic">p</Emphasis>-summable right-hand side |
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Authors: | Pierre-Etienne Druet |
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Institution: | (1) Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599, USA |
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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. |
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Keywords: | |
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