LAUSR

We prove some results regarding the existence of solutions on $$L^1$$L1-spaces to a nonlinear mono-energetic singular transport equation (i.e., transport equation with unbounded collision frequency and unbounded collision operator) in slab geometry. Our approach consists in rewriting the problem as a fixed point one involving a nonlinear ws-compact operator and we use a recent fixed point theorem for this class of operators (see Theorem 2.10) to derive existence results. We present a detailed analysis for the case where the boundary conditions are modeled by specular reflections, while the problem with periodic boundary conditions is discussed succinctly, because, except some minor modifications, the arguments of proofs are almost the same.