Existence and Uniqueness Theorems for the Neutron Transport Equation

Abstract

In an attempt to understand the conditions under which the neutron transport equation has solutions, and the properties of those solutions, a number of existence and uniqueness theorems are proved. One finds that the properties of the solution are closely related to the boundedness of the source as well as to certain velocity‐space integrals of the scattering kernel. Both time‐dependent and time‐independent equations are considered as are also the time‐dependent and time‐independent adjoint equations. Although only a very few of all possible existence and uniqueness theorems for these equations are considered here, the work may serve as a guide to the treatment of similar problems.