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Integro‐differential equation modelling heat transfer in conducting, radiating and semitransparent materials
Author(s) -
Laitinen M. T.,
Tiihonen T.
Publication year - 1998
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19980325)21:5<375::aid-mma953>3.0.co;2-u
Subject(s) - work (physics) , heat transfer , monotone polygon , thermal radiation , radiative transfer , operator (biology) , mathematics , heat equation , partial differential equation , boltzmann equation , mathematical analysis , thermodynamics , physics , chemistry , geometry , optics , biochemistry , repressor , gene , transcription factor
In this work we analyse a model for radiative heat transfer in materials that are conductive, grey and semitransparent. Such materials are for example glass, silicon, water and several gases. The most important feature of the model is the non‐local interaction due to exchange of radiation. This, together with non‐linearity arising from the well‐known Stefan–Boltzmann law, makes the resulting heat equation non‐monotone. By analysing the terms related to heat radiation we prove that the operator defining the problem is pseudomonotone. Hence, we can prove the existence of weak solution in the cases where coercivity can be obtained. In the general case, we prove the solvability of the system using the technique of sub and supersolutions. © 1998 B. G. Teubner Stuttgart–John Wiley & Sons Ltd.