Diffusive limits of the steady state radiative heat transfer system: Boundary layers

In this paper, we study the diffusive limit of the steady state radiative heat transfer system for non-homogeneous Dirichlet boundary conditions in a bounded domain with flat boundaries. By taking account of the boundary layers, a composite approximate solution is constructed using asymptotic analysis. The convergence to the composite approximate solution in the diffusive limit is proved using a Banach fixed point theorem. The major difficulty lies in the nonlinear coupling between elliptic and kinetic transport equations. To overcome this difficulty, a spectral assumption is proposed to ensure the linear stability of boundary layers. Moreover, a combined L²-L^∞ estimate and the Banach fixed point theorem are used to obtain the convergence proof. This result extends our previous work [6] for the well-prepared boundary data case to the general boundary date.