On the diffusive limits of radiative heat transfer system I: well prepared initial and boundary conditions

Abstract

We study the diffusive limit approximation for a radiative heat transfer system under three different types of boundary conditions. We prove the global existence of weak solutions for this system by using a Galerkin method. Using the compactness method, averaging lemma and Young measure theory, we prove that the weak solution converges to a nonlinear diffusion model in the diffusive limit. Under more regularity conditions on the limit system, the diffusive limit is also analyzed by using a relative entropy method. In particular, we get a rate of convergence. The initial and boundary conditions are assumed to be well-prepared in the sense that no initial and boundary layer exist. Contents 42 Appendix A. Lemmas used in the Compactness Method 44 Appendix B. Basis in L 2 (Ω × S 2 ) 46