neutron flux; analytical solution; cross sections; semigroup of operators; asymptotic behaviour; linear Boltzmann equation; neutron transport; initial value problem; non-negative asymptotic solution; critical system
In this paper, the initial-value problem, the problem of asymptotic time behaviour of its solution and the problem of criticality are studied in the case of linear Boltzmann equation for both finite and infinite media. Space of functions where these problems are solved is chosen in such a vay that the range of physical situations considered may be so wide as possible. As mathematical apparatus the theory of positive bounded operators and of semigroups are applied. Main results are summarized in three basic theorems.
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