The radiative transfer equations: Existence of solutions and diffusion approximation under accretivity assumptions — A survey

In this paper, we recall some results on the radiative transfer equations: Or in short Under some monotonicity assumptions introduced in [16] and which are compatible with a singularity of σν: σν (0) = +∞, the operator Qε is proved to be T-accretive. This yields an existence result for the evolution equation. The stability induced by the accretivity allows to prove that, for particular entering flux, (Eε, Iε) converges in L1, as ε goes to 0, to the solution of the Rosseland equation When the problem is independent of ν, we give a complete treatment of this approximation involving the boundary layer effect.