Nonlinear Multigroup Neutron-Flux System: Blow up, Decay, and Steady States

[[abstract]]This article investigates a nonlinear system of partial differential equations describing multigroup neutron-flux reaction-diffusion inside a nuclear fission reactor. The neutrons are divided into n energy groups, with fission and scattering rates dependent on temperature, which gives rise to the (n+1)th equation. Cases concerning directly coupled and down scattering, when group transfers only occur from higher to lower energy groups, are considered. Quantitative conditions on the various fission and scattering rates are found for eventual ``blowup'' and ``decay'' of neutron concentrations. Finally, a system with fission and scattering rates dependent on neutron density is also investigated. Sufficient conditions for positive nontrivial steady state are found.[[fileno]]2060128010014[[department]]工程與系統科學