Bifurcating Solutions and Stabilities for Multigroup Neutron Fission Systems with Temperature Feedback

This article studies a system of reaction-diffusion equations describing neutron fission in a reactor. There are m equations for neutrons in m energy groups and a last equation for temperature. The interaction rates depend on temperature feedback. It is shown that a nontrivial positive steady state bifurcates from zero as the size of the reactor varies. The asymptotic stability of the positive solution is also shown. Methods in bifurcation theory, linearized stability, and sectorial operators are used. The results improve some existing theories on the subject.