Stability analysis of the neutron transport equation with temperature feedback

Abstract

This paper discusses the stability and instability of neutron transport in a reactor system where positive temperature feedback is taken into consideration. The feedback effect is considered only through the multiplication factor in the neutron transport equation. This consideration leads to a coupled system of nonlinear partial integrodifferential equations of neutron transport and heat conduction. The investigation of this coupled nonlinear initial boundary-value problem is based on the existence-comparison theorem established in an earlier paper in which an iterative scheme for the determination of the solution is given. It is shown in this paper that by constructing a suitable pair of the comparison functions, called upper and lower solutions, as two distinct initial iterations, the corresponding sequences converge monotonically from above and below, respectively, to a unique solution of the system. Under certain conditions on the multiplication factor, the property of upper and lower solutions determines the asymptotic behavior of the solution and leads to stability or instability of the system. A stability region for the zero steady state and an instability region of the system are also given.