Über Anfangs-und Eigenwertprobleme aus der Neutronentransporttheorie

Abstract

Based on the theory of semi-groups in Hilbert space, a proof is given for the existence of a unique solution of an abstract Cauchy problem arising in the transport theory of mono-energetic neutrons, corresponding to the time-dependent linear Boltzmann equation in the general three-dimensional geometry. The spectral properties of the Boltzmann operator are investigated, an explicit representation of the solution is obtained by the perturbation theory for semi-groups of linear operators and alternatively an expansion in a series of eigenfunctions is given.