Mathematical Modelling of Neutron Production and Absorption in Material Media

Neutron populations in material media are controlled by competing mechanisms of production, ab-sorption, and leakage. In this work, a simplified mathematical model is proposed to describe the timeevolution of neutron density by ordinary differential equations. Starting from a balance law, a linearmodel with source and absorption terms is derived, and an extended nonlinear model including quadraticlosses is also discussed. Analytical solutions, equilibrium states, asymptotic behaviour, and integral in-terpretations are obtained. The model provides a compact description of neutron balance and offers auseful introductory framework for nuclear engineering and reactor physics.