Review of mathematical theory of neutron transport equations

A brief summary is presented on neutron transport theory, limited to spectral theory, exact solutions and approximate treatment of transport equations. The first part of this report covers spectral theoretic studies of initial value problems. The spectrum of neutron wave propagation and the relaxation length of neutron diffusion is not discussed. In the second part, various anaytical methods of solving steady state problems are described, most of which are a direct outgrowth of the well-known Case method. Finally, the mathematical theory of finite difference methods for deriving approximate solutions of the transport equation is summarized, with emphasis on convergence and stability. (author)