On nonlinear neutron transport equations

AbstractThe purpose of this paper is to investigate a class of time-dependent neutron transport equations in which the total and differential scattering cross sections are nonlinear functions of neutron density function. Sufficient conditions on the nonlinear cross sections are given to insure the existence, uniqueness and asymptotic stability of a solution in one, two, or three-dimensional space domains under various boundary and initial conditions. The approach to the problem is based on abstract analysis on nonlinear evolution equations which are closely related to nonlinear semigroup theory