Thompson, M.; de Vilhena, M. T.; Bodmann, B. E. J. Existence theory for radiative flows. (English) Zbl 1156.80371 Transp. Theory Stat. Phys. 37, No. 2-4, 307-326 (2008). Summary: We consider the coupling of radiative heat transfer equations and the energy equation for the temperature \(T\) of a compressible fluid occupying a bounded convex region \(D\) with smooth boundary. Using the technique of upper and lower sequences associated with integro-parabolic equations, we establish the existence and uniqueness of a solution \(T\), \(0\leq \Lambda_- \leq T(x,t) \leq \Lambda_+ < \infty\) with corresponding radiative intensity \(I(x,\Omega,\nu,t)\) where the total incident radiation satisfies \(\int_{S^2}I(x,\Omega,\nu,t)d\Omega = S_g B(\nu,t)+S_b B(\nu,T_b)\), and where \(S_b\) and \(S_g\) are positivity preserving linear operator, \(T_b\) is the external temperature of the boundary, and \(B\) is Planck’s function. We also establish certain energy estimates for \(T\). Cited in 4 Documents MSC: 80A20 Heat and mass transfer, heat flow (MSC2010) 76R10 Free convection 78A40 Waves and radiation in optics and electromagnetic theory 45K05 Integro-partial differential equations 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics Keywords:conductive-radiative heat transfer; fluid flows; upper and lower solutions; parabolic integro-differential evolution equations PDFBibTeX XMLCite \textit{M. Thompson} et al., Transp. Theory Stat. Phys. 37, No. 2--4, 307--326 (2008; Zbl 1156.80371) Full Text: DOI References: [1] DOI: 10.1016/0362-546X(79)90047-6 · Zbl 0416.45008 · doi:10.1016/0362-546X(79)90047-6 [2] Dautray R., Mathematical Analysis and Numerical Methods: Evolution Problems II 6 (2000) · Zbl 0956.35001 [3] DOI: 10.1504/PCFD.2004.004087 · doi:10.1504/PCFD.2004.004087 [4] DOI: 10.1080/00411459608204839 · Zbl 0857.45009 · doi:10.1080/00411459608204839 [5] DOI: 10.1006/jcph.2002.7210 · Zbl 1016.65105 · doi:10.1006/jcph.2002.7210 [6] Latrach K., Comptes Rendus de l’Académie des Sciences 333 pp 433– (2001) · Zbl 1009.45009 · doi:10.1016/S0764-4442(01)02073-0 [7] Modest M., Radiative Heat Transfer (1993) [8] DOI: 10.1142/9789812819833 · doi:10.1142/9789812819833 [9] Pao C., Nonlinear Parabolic and Elliptic Equations (1992) · Zbl 0777.35001 [10] Temam R., Infinite Dimensional Dynamical System in Mechanics and Physics (1988) · Zbl 0662.35001 [11] DOI: 10.1081/TT-200053941 · Zbl 1085.80002 · doi:10.1081/TT-200053941 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.