Abstract This paper addresses the diffusive limit of the nonlinear radiative heat transfer system in a curved boundary domain. Our major contribution is the development of a groundbreaking geometric correction for the boundary layer problem, which results in a valid approximate solution in the L ∞ sense. This advancement significantly extends the earlier result on the flat boundary case (Ghattassi et al 2023 J. Math. Pures Appl. 9 181–215) to complex domains with curved boundaries and the earlier result on geometric corrections on the single linear radiative transfer equation (Wu and Guo 2015 Commun. Math. Phys. 336 1437–553) to a nonlinear system of equations. Importantly, we show that the spectral assumption from (Ghattassi et al 2023 Arch. Ration. Mech. Anal. 247 52) for flat boundaries remains valid, ensuring stability with geometric corrections. Additionally, we rigorously proved the convergence of the solutions to a derived approximation system, taking into account boundary layers and geometric corrections. In general, this work represents a significant leap forward in understanding and applying radiative heat transfer systems to more complex scenarios.
Ghattassi et al. (Thu,) studied this question.