Dynamics of a parabolic problem arising in nuclear engineering

Abstract

This paper analyzes the dynamics of a spatially heterogeneous parabolic system, which is a refinement of a classical prototype model in Nuclear Engineering proposed by W. E. Kastenberg and P. L. Chambré [13], introduced to study the interactions between the density of fast neutrons and the temperature in the reactor. The dynamics is completely characterized within the ranges of values of the parameters where the model does not admit a positive steady state, as well as in the region where it admits a positive steady state and the system can be transformed, through an appropriate change of variable, into an irreducible cooperative system, as discussed by J. López-Gómez and M. Molina-Meyer [19], where it is shown that the coexistence state is a global attractor.