2001
DOI: 10.1090/qam/1866555
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Conductive-radiative heat transfer in grey materials

Abstract: Abstract.We study the well-posechiess of a class of models describing heat transfer by conduction and radiation.For that purpose we propose an abstract mathematical framework that allows us to prove existence, uniqueness and the comparison principle for the weak solution with minimal or almost minimal a priori assumptions for the data. The theory covers different types of grey materials, that is, both semitransparent and opaque bodies as well as isotropic or nonisotropic scattering/reflection provided that the… Show more

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Cited by 43 publications
(61 citation statements)
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“…Analogous to (2.1) problems arise in conductive-radiative heat transfer, see, for instance, M. Laitinen and T. Tiihonen [9], K. Birgelis [3], C. Mayer and others [10] and references therein.…”
Section: Consider the Problem (With Respect Tomentioning
confidence: 99%
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“…Analogous to (2.1) problems arise in conductive-radiative heat transfer, see, for instance, M. Laitinen and T. Tiihonen [9], K. Birgelis [3], C. Mayer and others [10] and references therein.…”
Section: Consider the Problem (With Respect Tomentioning
confidence: 99%
“…In [3,9] it was shown that if functions f 0 , g, u * belong to a given set M 0 , elements of which are of practical interest, then the solutions u 0 of (2.1) are bounded and there exists a constant u max such that…”
Section: Modified Problemmentioning
confidence: 99%
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