A three-dimensional neutron transport problem

Abstract

We study the stationary neutron transport Boltzmann equation as applied to a three-dimensional system D, made by a rectangular multiplying core surrounded by a finite reflector, in both the Lebesgue space L2(D) and the space C (D) (with the sup norm). As a result of this analysis, we prove some basic properties, such as the continuous dependence of the neutron flux on the parameters characterizing both the geometrical and the material properties of the system and the continuous and monotonic dependence of the average number of secondary neutrons per collision in the core on these parameters.