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.
"Reaction-diffusion systems for multigroup neutron fission with temperature feedback: positive steady-state and stability." Differential Integral Equations 10 (4) 739 - 756, 1997. https://doi.org/10.57262/die/1367438639