ASYMPTOTIC EXPANSION AND ASYMPTOTIC BEHAVIOR OF THE SOLUTION FOR THE TIME-DEPENDENT NEUTRON TRANSPORT PROBLEM IN A SLAB WITH GENERALIZED BOUNDARY CONDITIONS

摘要

In this paper,the time-dependent neutron transport integro-differential equationin a nonuniform slab with generalized boundary conditions and initial value is considered forgeneral cases concerned with an arbitrary nonhomogeneous medium possibly with cavity,withthe anisotropic scattering and fission,and with continuous energy varying from null to any finiteconstant or from one positive constant to another positive constant.We prove that the correspon-ding neutron transport operator A has finite Spectrum points in any strip {λ|β₁≤R（?）λ≤β₂}whereβ₂β1-λ*（λ* is the essential infimum of v∑（x,v））,and obtain the asymptotic expansion ofthe time-dependent solution which exists and is unique.Furthermore,we give the existence ofthe dominant eigenvalue and indicate the asymptotic behavior of the neutron density as t→+∞.