Reaction-diffusion systems for multigroup neutron fission with temperature feedback: positive steady-state and stability

Abstract

We consider a system of reaction-diffusion equations describing the dynamics of fission reactors with temperature feedback. There are $m$ equations for the neutrons in $m$ energy groups and a last temperature equation. We use the bifurcation method to find positive steady-states for the system which is not symmetric. We then analyze the linearized stability of the steady-state as a solution of the full system of $m+1$ parabolic equations. The asymptotic stability of the steady-state solution is proved by means of a stability theorem for sectorial operators.