Abstract
We consider the coupling of radiative heat transfer equations and the energy equation for the temperature Tof 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 ≤ Λ− ≤ T(x,t) ≤ Λ+ < ∞ with corresponding radiative intensity I(x,Ω,ν,t) where the total incident radiation satifies ∫S2 I(x,Ω,ν,t)dΩ = Sg B(ν,t)+Sb B(ν,Tb), and where Sb and Sg are positivity preserving linear operator, Tb is the external temperature of the boundary, and B is Planck's function. We also establish certain energy estimates for T.