Neutron Transport in a Nonuniform Slab with Generalized Boundary Conditions

Abstract

We prove the existence and the uniqueness of the solution of the initial-value problem for neutron transport in a nonuniform slab with generalized boundary conditions, which include the vacuum and the perfect reflection boundary conditions as particular cases. Moreover, we show that the position-dependent transport operator has at least one real eigenvalue and we indicate the asymptotic behavior of the neutron density as t → + ∞.