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The kinetics equations in a multiplying medium with free boundaries
Author(s) -
BelleniMorante A.,
Lauro G.
Publication year - 1990
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670130307
Subject(s) - mathematics , ordinary differential equation , multiplication (music) , differential equation , stability (learning theory) , mathematical analysis , neutron , slab , physics , combinatorics , nuclear physics , machine learning , geophysics , computer science
Abstract We study a mathematical model of neutron multiplication in a slab , by taking into account temperature feedback effects and considering one group of delayed neutrons. The thickness 2 a of is time dependent because of temperature variations due to the energy released by fissions. Starting from a quite detailed picture of the physical phenomena occurring in , we derive a system of three coupled ordinary differential equations for the total number of neutrons F̂ = F̂( t ), for the total number of precursors Ĉ = Ĉ( t ), and for the half‐thickness of , a = a ( t ). We finally examine some stability properties of such a system of ordinary differential equations.