Generalized solutions of the radiative transfer equations in a singular case

This paper is devoted to the study of the radiative transfer equations:[Figure not available: see fulltext.] First, we prove a global existence theorem, which allows a blow-up of the opacity σ_v(ℰ) when ℰ→0. Thus, it extends Mercier's previous result [13]. This proof relies mainly on a nonlinear version of Hille-Yosida theorem: see Crandall-Ligett [9]. Then, we prove the uniqueness of the semigroup solving (TR), and some regularity results (in the class of functions with bounded variation). Finally, we prove the convergence of some splitting algorithms associated to (TR).