Stability and instability of the energy dependent diffusion system in reactor dynamics

Abstract

AbstractThe purpose of this paper is to give a systematic analysis for the linear energy dependent diffusion system in reactor dynamics, taking into consideration of delayed neutrons. This analysis includes the existence of a unique positive solution for the time dependent system, the asymptotic behaviour of the solution as t → ∞, the stability and instability of steady‐state solutions, and the existence and uniqueness of a steady‐state solution for the time‐independent system. Using the notion of upper and lower solution, we establish some threshold conditions for insuring the asymptotic behaviour of the solution and the stability and the instability of any given unperturbed solution, including steady‐state solution. In fact, these conditions characterize the stability and the instability property of the solution, and yield a bifurcation result in terms of either the size of the diffusion domain or the physical parameters of the diffusion medium. We also discuss the case without the effect of delayed neutrons.